Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter

Ichiro Maruta; Toshiharu Sugie

REVIEW 3 major objections 5 minor 30 references

Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Fast sampling makes state-variable-filter identification errors vanish

desk verdict A serious empirical paper with a real proof gap: the O(h) variance claim for the actual SVF estimator is asserted, not proven, because the regressor D_F is stochastic and correlated with the equation error. read the letter →

arxiv 2506.03650 v1 pith:46PE2PJP submitted 2025-06-04 eess.SY cs.SY

Ichiro Maruta , Toshiharu Sugie This is my paper · ORCID

classification eess.SYcs.SY

keywords Continuous-timemodelsClosed-loopidentificationEstimationerrorvarianceFastsamplingStatevariablefilterSystemAliasingnoiseMIMOsystems

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the classical rule of sampling about ten times the system bandwidth is not a fundamental limit: when identification is done in continuous time with a state variable filter, the variance of the least-squares parameter estimate is proportional to the sampling interval $h$, so making $h$ smaller monotonically improves accuracy. The scaling is claimed to hold even when the noise is colored, correlated with the input, or carries constant offsets, and it applies in closed-loop operation with an unknown, possibly nonlinear controller. A sympathetic reader should care because this turns a single linear regression, with no solver sophistication and no controller information, into a method that can identify unstable MIMO plants under heavy noise. The paper supports the claim with simulations in stable, unstable, offset-ridden, and MIMO closed-loop settings.

What carries the argument

The machine is the SVF-like least-squares estimator: pass the measured input $u$ and output $y$ through a bank of strictly proper filters $F(p)$, form $Y_A$ from the filtered $n$-th derivative of $y$ and $D_F$ from the filtered lower derivatives of $u$ and $y$, and compute $\hat{\theta} = (D_F^\top D_F)^{-1} D_F^\top Y_A$. Its work is to make the regression asymptotically deterministic: the filter $H_2$-norm lemma gives filtered noise variance $O(h)$, while the deterministic signal component is preserved, so Theorem 1 applies. A numerator factor $p$ in $F(p)$ also nullifies constant offsets by making the filter's steady-state response to a constant vanish.

What would settle it

Simulate the paper's closed-loop unstable plant P1 with a colored disturbance concentrated in the passband of the SVF filter, then compute the mean squared parameter error for $h = 1$ ms, $0.1$ ms, and $0.01$ ms; if the log-log slope departs from $-1$ or flattens, the deterministic-regressor assumption is the bottleneck.

Watch

Extended reading notes

Core claim

The central claim is Theorem 1: for the regression $Y_h = \Phi_h \theta^\star + V_h$, if the regressor matrix $\Phi_h$ is deterministic and well conditioned as $h \to 0$ and the total noise energy $\operatorname{Tr}(\Sigma_h)$ is $O(1)$, then the least-squares estimate satisfies $\operatorname{Tr}(\operatorname{Cov}(\hat{\theta})) = O(h)$. The paper's application claim is that the SVF regressors inherit exactly these conditions because they are outputs of continuous-time filters, so they neither lose rank, unlike discrete-time regressors as $h \to 0$, nor carry noise whose variance fails to shrink. Lemma 1 supplies the mechanism: for any strictly proper filter, the variance of filtered white noise is approximately $h$ times the continuous-time $H_2$ norm. The paper concludes from this that fast sampling plus the SVF-like method is a general-purpose cure for closed-loop identification, offset rejection, and unstable MIMO identification, requiring only one least-squares solve.

Load-bearing premise

The result assumes the noisy regressor matrix can be treated as deterministic as the sampling interval goes to zero; the actual SVF bias comes from the correlation between that noise and the output error, and the paper does not derive the rate at which that correlation vanishes.

Editorial extensions

If this is right

As the sampling interval $h$ is decreased, SVF least-squares identification improves without a lower limit, unlike discrete-time ARX or SSARX methods, which deteriorate once $h$ is too small.
Closed-loop identification of unstable plants no longer requires knowledge of the controller, the reference signals, or any nonlinearity in the feedback path.
Constant offsets in input disturbance and output measurement are rejected by choosing a filter with a zero at $p=0$, with no need to estimate the offset sizes.
The result carries over to MIMO systems with a common-denominator polynomial model, requiring only one least-squares fit over all channels.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The $O(h)$ argument should extend to any continuous-time estimator built from filtered regressors whose filters are strictly proper, such as instrumental-variable variants, but the paper only proves it for plain least squares with an effectively deterministic regressor.
A practical design rule suggested by the paper is the opposite of the classical one: sample as fast as hardware and conditioning allow, and use continuous-time filtering in place of effortful pre-sampling anti-aliasing.
The theorem's deterministic-regressor assumption leaves the classical SVF bias unevaluated; whether the $O(h)$ slope survives in practice may depend on how fast the noise-regressor correlation decays, which the filter's roll-off controls.
A hardware experiment without anti-aliasing filters would be the sharpest test, because the aliasing-noise mechanism the paper identifies should appear as the dominant $O(h)$ floor.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Good paper to know about. The claim is that sampling much faster than the usual rule turns the old, biased SVF method into a workhorse for hard identification problems: closed-loop, unstable, offset-ridden, MIMO, all with one least-squares fit. The experiments support this: they sweep h over four decades, show the error going down as O(h) to O(h^2), and compare fairly against ARX/SSARX. The nu-gap metric for unstable plants is sensible. I buy the empirical phenomenon.

What is genuinely new is the observation that fast sampling, by shrinking the variance of filtered noise while keeping the signal-to-noise ratio fixed, removes the bias that has kept SVF out of mainstream use. The scaling theorem itself (Theorem 1) is a few lines of norm inequalities and is fine. The problem is in the application. In Section III-D.1 the authors need to go from 'each filtered noise component has variance O(h)' to 'we can treat D_F as effectively deterministic.' That step is asserted, not proved. D_F contains the same filtered noise that appears in the equation error Y_A; in closed loop the correlation is structural. The classical SVF bias is exactly the non-zero expectation of (D_F^T D_F)^{-1} D_F^T e. Per-entry variance O(h) does not rule out an O(1) normalized cross-term, because the sums contain O(1/h) terms. So Theorem 1 does not currently cover the actual estimator in Eq. (42). The numerical evidence is consistent with the missing bound holding, and a competent referee could likely extract the right rate from the authors, but as written the proof is incomplete.

There is also an untested caveat: the O(h) law relies on total noise energy staying O(1) as h shrinks, which holds for aliased white noise without anti-aliasing filters, but real bandlimited noise would stop delivering O(h) gains at some point. The authors do not discuss that saturation.

Bottom line: this is a serious paper, worth refereeing and probably worth publishing after the proof gap is closed. The applications are real and the experiments are honest. I would read it carefully and ask for the missing correlation bound.

Who it is for: anyone working in continuous-time identification or closed-loop identification. The idea is simple enough to be useful in practice. Recommendation: send to peer review. The gap is real but repairs are plausible.

Referee Report

3 major / 5 minor

Summary. The paper claims that using a state variable filter (SVF)-like least squares method for continuous-time system identification, the variance of the parameter estimation error scales as O(h) with the sampling interval h, and that this scaling holds even with colored noise, noise correlations, closed-loop operation, measurement offsets, and unstable MIMO plants. The theoretical basis is Theorem 1, which gives an O(h) covariance bound for least squares with a deterministic regressor and bounded total noise energy. The authors then apply Theorem 1 to the SVF estimator by asserting that the noisy regressor matrix D_F can be treated as deterministic in the limit h -> 0. Numerical experiments on several plants, including an unstable MIMO system, show error decreasing as h decreases, seemingly confirming the O(h) scaling.

Significance. If the central claim is correct, the result is practically important: it would mean that fast sampling plus a simple, classical SVF least squares fit can solve closed-loop identification, offset rejection, and unstable MIMO identification without controller knowledge or specialized algorithms. The paper is clearly written and the numerical study is extensive, including a meaningful metric (ν-gap) that shows improvement of SVF over discrete-time ARX/SSARX as h decreases. However, the central theoretical step—applying a theorem about deterministic regressors to an estimator with a stochastic, noise-correlated regressor—is not justified in the manuscript, and the noise model underlying the O(h) scaling is too narrow to support the abstract's 'independent of noise color' claim. These issues are load-bearing, so the paper needs substantial revision before the claim is established.

major comments (3)

[Section III-D.1, Eq. (42)] The proof that the SVF least squares estimator obeys the O(h) covariance bound is missing. Theorem 1 requires the regressor Φ_h to be deterministic, but in (42) the regressor D_F is constructed from filtered noisy measurements and is therefore stochastic and, in closed loop, correlated with the equation error in Y_A because both contain filtered versions of the same noises w and η. The sentence 'we can treat D_F as effectively deterministic' is an assertion, not a derivation; the classical SVF bias arises precisely from this correlation. To invoke Theorem 1 one must prove, not assert, that the normalized cross terms vanish at a known rate, for example that (h/T_f) E[D_F^T (Y_A - D_F θ*)] = O(h) and that (h/T_f) D_F^T D_F converges to a positive definite limit in a suitable sense. Until this calculation is supplied, the O(h) variance claim for the actual SVF estimator is unproven.
[Section II-B, Lemma 1 and Section II-C, Assumption (A2)] The O(h) variance scaling in Lemma 1 is derived for a discrete-time white-noise input whose per-sample variance is fixed. For bandlimited or continuous-time colored noise, the per-sample variance of the filter output does not decrease once h is below the noise correlation time; then the total noise energy over a fixed interval T_f scales as O(1/h), violating Assumption (A2) and invalidating the O(h) covariance conclusion. The paper's claim that the scaling holds 'independent of noise color' is therefore not supported. The numerical experiments avoid this regime because the noise is generated by sampling and holding white noise with a fixed 5×10^-6 s update interval, and h is never smaller than 10^-5 s. Please either restrict the claim to the discrete-time white-noise model with per-sample variance independent of h, or provide an analysis of bandlimited noise showing when Tr(Σ_h)=O(1) remains valid.
[Section III-D.2, offset handling] The offset-removal procedure relies on the filtered version of a constant signal decaying as t → ∞, and the paper states that discarding data before t ≥ 15 s suffices. However, this is a heuristic choice: the decay rate depends on the chosen filter and the value of the offset, and the discarded interval is not part of the formal problem statement. The paper should either specify how the settling time is chosen or note that the method requires a user-selected truncation that is not covered by the O(h) analysis.

minor comments (5)

[Section II-C, Remark 2] In Remark 2, the text says 'Tr(Cov(θ̂)) = Σ E[v(kh)^2]', but the quantity being constrained by Assumption (A2) is the total noise variance Tr(Σ_h), not the covariance of the estimate. Please correct the notation.
[Section II-B, Lemma 1] The proof of Lemma 1 uses '≈' without explicit error bounds. Please state the regularity assumptions on F(s) (stable, strictly proper, with minimal realization) and give an asymptotic expansion such as ||F_h(z)||_2^2 = h ||F(s)||_2^2 + O(h^2) as h → 0, with a brief justification.
[Section III-C, Eqs. (37)-(38)] The symbol E is used both for the expectation operator and for the residual vector in (37)-(38). This is confusing; please use a different symbol for the residual, such as R or ε.
[Section IV-B, Eq. (70)] The indexing in the definition of the held signals ̅u(t) and ̅y(t) is introduced only here; please define it earlier in Section III and ensure the round/ceil notation is consistent with the sampling instants t=k h used elsewhere.
[Section V, Conclusions] The conclusion states the scaling is valid 'even with the presence of colored noise or the noise correlations between variables', but the theoretical and numerical sections only treat additive noise that is white at the sampling instants with independent MIMO channels. Please soften this sentence or provide supporting analysis for correlated variables.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the O(h) covariance bound follows from explicit assumptions (A1)-(A2), and the only self-citation is non-load-bearing.

full rationale

Theorem 1 is derived directly from the stated assumptions: (A1) gives (Phi_h^T Phi_h)^{-1} = O(h) and cond = O(1), and (A2) gives ||Sigma_h|| = O(1), so the norm bound on Cov(theta_hat) in Eq. (20)-(22) follows by standard norm inequalities with no fitted parameter and no imported result. The application of Theorem 1 to the SVF estimator (42) is not circular, but it does contain a gap: Section III-D.1 asserts that because each filtered-noise component has variance O(h), 'we can treat D_F as effectively deterministic' and then identifies Y_h = Y_A, Phi_h = D_F. This treats a stochastic regressor as deterministic without bounding the correlation between the noise in D_F and the equation-error noise in Y_A; that is the classical SVF bias mechanism. However, the paper does not define the conclusion into the assumption or rename a fitted quantity as a prediction; it is an unproven regularity step, not a circular reduction. The only self-citation, [30], is used to note the equivalence of the fixed-pole observer and SVF and to motivate that SVF can handle unstable closed-loop systems; this is not load-bearing for the central O(h) scaling claim. The numerical experiments in Section IV are external checks rather than fitted inputs. Overall, the central derivation is self-contained under its assumptions, with the noted stochastic-regressor gap being a rigor concern rather than circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard least squares and filter theory; no new entities are invented. The free parameters are the hand-chosen SVF filters in the experiments, and the main unproven assumption is the deterministic-regressor treatment.

free parameters (1)

SVF filter coefficients in experiments = F(s)=s/((s+1)(s^2+1.8s+1)) for P1-P3; F(s)=1/((s+1)^2((s+0.2)^2+1.992^2)) for P4
Hand-chosen filter parameters; the theory only requires stability and sufficient relative degree, but the numerical accuracy and offset rejection in the examples depend on these choices and no tuning rule is provided.

assumptions (4)

standard math Riemann sum approximation in Lemma 1: ||F_h(z)||_2^2 is approximately h ||F(s)||_2^2 for h << 1
Used to conclude filtered noise variance is O(h); stated with a heuristic proof and no error bound.
domain assumption Continuous-time regressors satisfy A1: (h/Tf) D_F^T D_F -> R positive definite (Remark 1)
Requires the filtered input-output signals to be persistently exciting and continuous on almost every interval; assumed, not verified for the closed-loop examples.
domain assumption Total filtered noise energy is O(1) as h -> 0 (Assumption A2)
Implied by the filtered noise per-sample variance being O(h); this holds for white noise with power above the Nyquist rate but fails for finite-bandwidth noise once h is below the noise correlation time, so the O(h) law is not universal.
ad hoc to paper D_F can be treated as deterministic in the limit h -> 0 (Section III-D.1)
This is the key unproven step connecting Theorem 1 (deterministic regressors) to the actual SVF estimator with noisy regressors; the paper asserts it without proof.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter." pith.science (2026). https://pith.science/paper/46PE2PJP

@misc{pith2026250603650,
  author       = {Pith},
  title        = {Pith review of: Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/46PE2PJP}},
  note         = {Machine review of arXiv:2506.03650}
}

abstract

This paper investigates the effects of setting the sampling frequency significantly higher than conventional guidelines in system identification. Although continuous-time identification methods resolve the numerical difficulties encountered in discrete-time approaches when employing fast sampling (e.g., the problems caused by all poles approaching unity), the potential benefits of using sampling frequencies that far exceed traditional rules like the "ten times the bandwidth" guideline remained largely unexplored. We show that using a state variable filter (SVF)-like least squares approach, the variance of the estimation error scales as $O(h)$ with the sampling interval $h$. Importantly, this scaling holds even with colored noise or noise correlations between variables. Thus, increasing the sampling frequency and applying the SVF method offers a novel solution for challenging problems such as closed-loop system identification and measurements with offsets. Theoretical findings are supported by numerical examples, including the closed-loop identification of unstable multi-input multi-output (MIMO) systems.

Figures

Figures reproduced from arXiv: 2506.03650 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 29 canonical work pages

[1]

Ljung, System Identification: Theory for the User , ser

L. Ljung, System Identification: Theory for the User , ser. Prentice Hall information and system sciences series. Prentice Hall PTR, 1999

work page 1999
[2]

On the choice of sampling rates in parametric identification of time series,

K. ˚Astr¨om, “On the choice of sampling rates in parametric identification of time series,” Information Sciences, vol. 1, no. 3, pp. 273–278, 1969. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0020025569800137

work page 1969
[3]

Improved finite word length charac- teristics in digital control using delta operators,

R. Middleton and G. Goodwin, “Improved finite word length charac- teristics in digital control using delta operators,” IEEE Transactions on Automatic Control, vol. 31, no. 11, pp. 1015–1021, 1986. MARUTA AND SUGIE: FAST SAMPLING FOR SYSTEM IDENTIFICATION: OVERCOMING NOISE, OFFSETS, AND CLOSED-LOOP CHALLENGES WITH SVF 13 10!5 10!4 10!3 10!2 10!1 SamplingIn...

work page 1986
[4]

Garnier and L

H. Garnier and L. Wang, Identification of Continuous-time Models from Sampled Data, ser. Advances in Industrial Control. Springer London, 2008

work page 2008
[5]

What does continuous-time model identification have to offer?

H. Garnier and P. Young, “What does continuous-time model identification have to offer?” IFAC Proceedings Volumes, vol. 45, no. 16, pp. 810–815, 2012, 16th IFAC Symposium on System Identification. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S1474667015380538

work page 2012
[7]

Closed-loop identification revisited,

U. Forssell and L. Ljung, “Closed-loop identification revisited,” Automatica, vol. 35, no. 7, pp. 1215–1241, 1999. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109899000229

work page 1999
[8]

Identification of unstable systems using output error and Box- Jenkins model structures,

——, “Identification of unstable systems using output error and Box- Jenkins model structures,” IEEE Transactions on Automatic Control , vol. 45, no. 1, pp. 137–141, 2000

work page 2000
[9]

Closed-loop identification via the fractional representation: Experiment design,

F. Hansen, G. Franklin, and R. Kosut, “Closed-loop identification via the fractional representation: Experiment design,” in 1989 American Control Conference, 1989, pp. 1422–1427

work page 1989

Show all 30 references

[10]

A virtual closed loop method for closed loop identification,

J. C. Ag ¨uero, G. C. Goodwin, and P. M. Van den Hof, “A virtual closed loop method for closed loop identification,” Automatica, vol. 47, no. 8, pp. 1626–1637, 2011. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109811002500

2011
[11]

A simple framework for identifying dynamical systems in closed-loop,

I. Maruta and T. Sugie, “A simple framework for identifying dynamical systems in closed-loop,” IEEE Access, vol. 9, pp. 31 441–31 453, 2021

2021
[12]

Subspace identification from closed loop data,

L. Ljung and T. McKelvey, “Subspace identification from closed loop data,” Signal Processing , vol. 52, no. 2, pp. 209–215, 1996, subspace Methods, Part II: System Identification. [Online]. Available: https://www.sciencedirect.com/science/article/pii/0165168496000540

1996
[13]

An overview of subspace identification,

S. J. Qin, “An overview of subspace identification,” Computers & Chemical Engineering , vol. 30, no. 10, pp. 1502–1513, 2006, papers form Chemical Process Control VII. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S009813540600158X

2006
[14]

Closed-loop subspace identification methods: an overview,

G. van der Veen, J.-W. van Wingerden, M. Bergamasco, M. Lovera, and M. Verhaegen, “Closed-loop subspace identification methods: an overview,” IET Control Theory & Applications , vol. 7, no. 10, pp. 1339–1358, 2013. [Online]. Available: https://ietresearch.onlinelibrary. wiley....

2013
[15]

Minimal realization of an unstable plant under feedback,

H. Tanaka and K. Ikeda, “Minimal realization of an unstable plant under feedback,” IFAC-PapersOnLine, vol. 54, no. 7, pp. 773–778, 2021, 19th IFAC Symposium on System Identification SYSID 2021. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S2405896321012295

2021
[16]

Application of a subspace model identification technique to identify LTI systems operating in closed-loop,

M. Verhaegen, “Application of a subspace model identification technique to identify LTI systems operating in closed-loop,” Automatica, vol. 29, no. 4, pp. 1027–1040, 1993. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/0005109893901042

1993
[17]

Subspace identification of closed loop systems by the orthogonal decomposition method,

T. Katayama, H. Kawauchi, and G. Picci, “Subspace identification of closed loop systems by the orthogonal decomposition method,” Automatica, vol. 41, no. 5, pp. 863–872, 2005. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109805000075

2005
[18]

Closed-loop subspace identification with innovation estimation,

S. J. Qin and L. Ljung, “Closed-loop subspace identification with innovation estimation,” IFAC Proceedings Volumes , vol. 36, no. 16, pp. 861–866, 2003, 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, The Netherlands, 27-29 August, 2003. [Online]. Availab...

2003
[19]

MOESP-type closed-loop subspace model identification method,

H. Oku, Y . Ogura, and T. Fujii, “MOESP-type closed-loop subspace model identification method,” Transactions of the Society of Instrument and Control Engineers , vol. 42, no. 6, pp. 636–642, 2006

2006
[20]

An approach to closed-loop subspace identification by orthogonal decomposition,

T. Katayama and H. Tanaka, “An approach to closed-loop subspace identification by orthogonal decomposition,” Automatica, vol. 43, no. 9, pp. 1623–1630, 2007. [Online]. Available: https://www.sciencedirect. com/science/article/pii/S0005109807001707

2007
[21]

On consistency of output-error closed-loop subspace model identification for systems compensated by general LTI controllers,

H. Oku and K. Ikeda, “On consistency of output-error closed-loop subspace model identification for systems compensated by general LTI controllers,” IFAC-PapersOnLine, vol. 54, no. 7, pp. 767–772, 2021, 19th IFAC Symposium on System Identification SYSID 2021. [Online]. Availabl...

2021
[22]

Subspace identification and ARX modeling,

M. Jansson, “Subspace identification and ARX modeling,” IFAC Proceedings Volumes , vol. 36, no. 16, pp. 1585–1590, 2003, 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, The Netherlands, 27-29 August, 2003. [Online]. Available: https://www.sciencedirect.co...

2003
[23]

Consistency analysis of some closed-loop subspace identification methods,

A. Chiuso and G. Picci, “Consistency analysis of some closed-loop subspace identification methods,” Automatica, vol. 41, no. 3, pp. 377–391, 2005, data-Based Modelling and System Identification. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S000510980400319X

2005
[24]

A rank minimization heuristic with application to minimum order system approximation,

M. Fazel, H. Hindi, and S. Boyd, “A rank minimization heuristic with application to minimum order system approximation,” in Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148) , vol. 6, 2001, pp. 4734–4739

2001
[25]

Hankel matrix rank minimization with applications to system identification and realization,

M. Fazel, T. K. Pong, D. Sun, and P. Tseng, “Hankel matrix rank minimization with applications to system identification and realization,” SIAM Journal on Matrix Analysis and Applications , vol. 34, no. 3, pp. 946–977, 2013. [Online]. Available: https://doi.org/10.1137/110853996

2013 doi
[26]

Nuclear norm system identification with missing inputs and outputs,

Z. Liu, A. Hansson, and L. Vandenberghe, “Nuclear norm system identification with missing inputs and outputs,” Systems & Control Letters, vol. 62, no. 8, pp. 605–612, 2013. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0167691113000819

2013
[27]

Frequency domain subspace identification using nuclear norm minimization and hankel matrix realizations,

R. S. Smith, “Frequency domain subspace identification using nuclear norm minimization and hankel matrix realizations,” IEEE Transactions on Automatic Control , vol. 59, no. 11, pp. 2886–2896, 2014

2014
[28]

N2SID: Nuclear norm subspace identification of innovation models,

M. Verhaegen and A. Hansson, “N2SID: Nuclear norm subspace identification of innovation models,” Automatica, vol. 72, pp. 57– 63, 2016. [Online]. Available: https://www.sciencedirect.com/science/ article/pii/S0005109816302163

2016
[29]

Nuclear norm-enhanced recursive subspace identification: Closed-loop estimation of rapid variations in system dynamics,

S. Navalkar and J. van Wingerden, “Nuclear norm-enhanced recursive subspace identification: Closed-loop estimation of rapid variations in system dynamics,” in 2016 American Control Conference (ACC) , 2016, pp. 936–941

2016
[30]

Direct closed-loop identification of continuous- time systems using fixed-pole observer model,

I. Maruta and T. Sugie, “Direct closed-loop identification of continuous- time systems using fixed-pole observer model,” in 2022 IEEE 61st Conference on Decision and Control (CDC) , 2022, pp. 2172–2177

2022
[31]

Frequency domain uncertainty and the graph topology,

G. Vinnicombe, “Frequency domain uncertainty and the graph topology,” IEEE Transactions on Automatic Control, vol. 38, no. 9, pp. 1371–1383, 1993. 14 IEEE TRANSACTIONS AND JOURNALS TEMPLATE 0.010.030.1 0.3 1 3 10 30 100SamplingIntervalh[ms] -5 -4 -3 -2 -1 0log10/8(^P;P?) SVFAR...

1993

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Ljung, System Identification: Theory for the User , ser

L. Ljung, System Identification: Theory for the User , ser. Prentice Hall information and system sciences series. Prentice Hall PTR, 1999

work page 1999

[2] [2]

On the choice of sampling rates in parametric identification of time series,

K. ˚Astr¨om, “On the choice of sampling rates in parametric identification of time series,” Information Sciences, vol. 1, no. 3, pp. 273–278, 1969. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0020025569800137

work page 1969

[3] [3]

Improved finite word length charac- teristics in digital control using delta operators,

R. Middleton and G. Goodwin, “Improved finite word length charac- teristics in digital control using delta operators,” IEEE Transactions on Automatic Control, vol. 31, no. 11, pp. 1015–1021, 1986. MARUTA AND SUGIE: FAST SAMPLING FOR SYSTEM IDENTIFICATION: OVERCOMING NOISE, OFFSETS, AND CLOSED-LOOP CHALLENGES WITH SVF 13 10!5 10!4 10!3 10!2 10!1 SamplingIn...

work page 1986

[4] [4]

Garnier and L

H. Garnier and L. Wang, Identification of Continuous-time Models from Sampled Data, ser. Advances in Industrial Control. Springer London, 2008

work page 2008

[5] [5]

What does continuous-time model identification have to offer?

H. Garnier and P. Young, “What does continuous-time model identification have to offer?” IFAC Proceedings Volumes, vol. 45, no. 16, pp. 810–815, 2012, 16th IFAC Symposium on System Identification. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S1474667015380538

work page 2012

[6] [7]

Closed-loop identification revisited,

U. Forssell and L. Ljung, “Closed-loop identification revisited,” Automatica, vol. 35, no. 7, pp. 1215–1241, 1999. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109899000229

work page 1999

[7] [8]

Identification of unstable systems using output error and Box- Jenkins model structures,

——, “Identification of unstable systems using output error and Box- Jenkins model structures,” IEEE Transactions on Automatic Control , vol. 45, no. 1, pp. 137–141, 2000

work page 2000

[8] [9]

Closed-loop identification via the fractional representation: Experiment design,

F. Hansen, G. Franklin, and R. Kosut, “Closed-loop identification via the fractional representation: Experiment design,” in 1989 American Control Conference, 1989, pp. 1422–1427

work page 1989