Pith. sign in

REVIEW 2 major objections 7 minor 22 references

New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases

T0 review · 2 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read DREM parameter estimators converge under excitation strictly weaker than persistence of excitation, and a new regressor choice provably speeds their transients.

desk verdict The finite-time alert estimator and the KRE unification are real contributions, but the advertised transient-performance guarantee in Prop 5 is wrong, so the paper needs major revision before it can be trusted. read the letter →

arxiv 1908.05125 v1 pith:4E5C6NNX submitted 2019-08-14 eess.SY cs.PFcs.SY

Romeo Ortega , Stanislav Aranovskiy , Anton A. Pyrkin , Alessandro Astolfi , Alexey A. Bobtsov This is my paper · ORCID
classification eess.SYcs.PFcs.SY MSC 93C4093E1093E12
keywords dynamicregressorextensionandmixingDREMparameterestimationlinearregressionmodelpersistenceofexcitationfinite-timeconvergenceadaptivecontroldiscrete-time
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

This paper strengthens dynamic regressor extension and mixing (DREM), a technique that converts one vector linear regression into m scalar regressions by multiplying through by the adjugate of an extended regressor matrix. It contributes two new designs for that matrix. The first, built from delayed regressor samples, makes the determinant's non-square-summability rather than persistence of excitation of the original regressor the condition for convergence, and this condition is genuinely weaker in discrete time. The second adds a feedforward term chosen as $\operatorname{adj}\{\Phi_0\}\varphi$ to the filtering operators and guarantees, through Sylvester's determinant formula, that every component of the parameter error is pointwise smaller than without the feedforward. The paper also gives a sliding-window finite-time estimator that keeps its finite-time property after parameter jumps, because its weighting signal can grow when new excitation arrives.

What carries the argument

The load-bearing object is the extended regressor matrix $\Phi=H[\varphi^\top]$ built by applying $m$ scalar linear operators to the regressor, together with its determinant $\Delta=\det\{\Phi\}$. Mixing multiplies the extended vector equation $Y=\Phi\theta$ by the adjugate matrix, which by $\operatorname{adj}\{M\}M=\det\{M\}I$ yields $m$ independent scalar regressions $Y_i=\Delta\theta_i$; the gradient estimators on these scalar regressions have parameter error dynamics $\dot{\tilde\theta}_i=-\gamma_i\Delta^2\tilde\theta_i$ in continuous time, so performance is governed entirely by $\Delta^2$. The paper's new results are mechanisms for shaping $\Delta$: a delay-window operator that turns $\Delta$ into a sum of rank-one regressor products, relaxing persistence of excitation; a feedforward gain $d(t)=\operatorname{adj}\{\Phi_0(t)\}\varphi(t)$ that adds a positive quadratic term to $\det\{\Phi\}$, improving transients; and a sliding-window weighting $w^D(t)$ built from the last $T_D$ seconds of $\Delta^2$, enabling reset-free finite-time convergence.

What would settle it

Run the continuous-time DREM estimator of Proposition 5 with filter parameters chosen so that $\det\{\Phi_0(t)\}<0$ for some interval while $\varphi(t)\neq 0$, apply $d(t)=\operatorname{adj}\{\Phi_0(t)\}\varphi(t)$, and plot $|\tilde\theta_i(t)|$ against the $d=0$ case: if the parameter-error absolute value is not pointwise smaller, the claimed transient improvement fails for that sign.

Watch

Extended reading notes

Core claim

The central discovery is that both the transient speed and the excitation requirements of DREM estimators are controlled by the scalar determinant $\Delta=\det\{\Phi\}$ of the extended regressor matrix, and that this determinant can be shaped by choosing the free operator $H$. In discrete time, taking $H$ to be a window of delayed regressor samples yields $\Phi(k)=\sum_{j=k+1}^{k+\bar K}\varphi(j-(1+\bar K))\varphi^\top(j-(1+\bar K))$, so $\varphi(k)\in PE$ implies $\Delta(k)\notin\ell^2$ and $\Delta(k)\in PE$, while a decaying scalar example shows $\Delta(k)\notin\ell^2$ without $\varphi(k)\in PE$; thus DREM converges under strictly weaker excitation than gradient or least-squares estimators. In continuous time, choosing the feedforward gain $d(t)=\operatorname{adj}\{\Phi_0(t)\}\varphi(t)$ in the general LTV operator makes $\det\{\Phi(t)\}=\det\{\Phi_0(t)\}+|\operatorname{adj}\{\Phi_0(t)\}\varphi(t)|^2$, so the squared determinant and hence the exponential decay rate in the scalar parameter error equations is pointwise larger than for $d=0$. Finally, replacing the memoryless weighting $w(t)$ by $w^D(t)=\exp(-\gamma\int_{t-T_D}^{t}\Delta^2(s)\,ds)$ yields the identity $[1-w^D]\theta=\hat\theta(t)-w^D\hat\theta(t-T_D)$, from which a finite-time estimate can be formed that revives when excitation reappears.

Load-bearing premise

The load-bearing premise is that increasing the determinant $\det\{\Phi_0(t)\}$ to $\det\{\Phi_0(t)\}+|\operatorname{adj}\{\Phi_0(t)\}\varphi(t)|^2$ always increases the decay rate $|\Delta|^2$ in the error equation, which is only guaranteed when the two determinants have the same sign; the paper does not establish that sign condition.

Editorial extensions

If this is right

  • In discrete time, DREM converges whenever $\Delta(k)$ is not square-summable, a condition strictly weaker than $\varphi(k)$ being persistently exciting; for example $\varphi(k)=(k+1)^{-1/4}$ is not PE but yields $\Delta(k)=(k+1)^{-1/2}\notin\ell^2$.
  • If $\Delta$ is persistently exciting, convergence is exponential, and this is also weaker than $\varphi$ being PE in the qualified window sense of Proposition 3.
  • The feedforward choice $d(t)=\operatorname{adj}\{\Phi_0(t)\}\varphi(t)$ makes each parameter error component strictly smaller at every time than the same DREM estimator without feedforward.
  • The new finite-time estimator uses $w^D(t)=\exp(-\gamma\int_{t-T_D}^{t}\Delta^2(s)\,ds)$; when $\Delta$ grows over a window of length $T_D$, $w^D$ grows, so the finite-time property is regained without resetting the estimator, allowing tracking of time-varying parameters.
  • The unified continuous- and discrete-time treatment makes the determinant $\Delta$ the single quantity to monitor for both classes of estimators.

Reading between the lines

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

  • Editorial inference: if the determinant sign condition in Proposition 5 can be enforced or replaced by $|\det|$, the transient-improvement guarantee would extend to arbitrary sign; a natural test is to rerun the simulation with $\Phi_0$ chosen with negative determinant and compare error curves.
  • Editorial inference: the delay-window construction of Proposition 3 suggests a continuous-time analogue where convergence is guaranteed by an integral-over-window condition on $\Delta$ rather than by PE; the paper leaves this extension to future work.
  • Editorial inference: the same sliding-window $w^D$ mechanism could be applied to other DREM-based adaptive controllers and observers wherever parameter jumps or intermittent excitation are expected, since it removes the need for resets.
  • Editorial inference: because the determinant $\Delta$ is scalar, it could serve as a real-time excitation monitor or as an excitation-injection target in composite adaptive control; this is not discussed in the paper.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. The paper studies dynamic regressor extension and mixing (DREM) parameter estimators for linear regression models. Its main contributions are: (i) a unified presentation of continuous-time and discrete-time DREM; (ii) two new extended regressor constructions, one based on a sliding window in discrete time, claimed to achieve convergence under excitation strictly weaker than persistency of excitation (Prop. 3), and one adding a feedforward term d(t) to the mixing operator, claimed to guarantee a quantifiable transient performance improvement (Prop. 5); and (iii) a new finite-time convergent (FTC) estimator based on a sliding-window regressor that retains alertness to time-varying parameters (Prop. 7). The paper also shows that Kreisselmeier's regressor extension is a particular case of the proposed generalized operator. Simulations are presented for the transient-improvement and FTC claims.

Significance. If the weaker-than-PE convergence result and the alert FTC scheme were correct, they would be valuable for adaptive control and identification, where PE is a major bottleneck. The generalized LTV operator framework and the explicit determinant identities are useful conceptual tools, and the proofs of Props. 3 and 7 are self-contained and largely first-principles. However, the transient-improvement guarantee in Prop. 5 is false, and the simulation formula for the new FTC estimator is inconsistent with the theorem. Since the transient-improvement claim is central to the abstract's advertised contribution, the paper cannot be accepted in its present form; the remaining sound ideas are worth pursuing after a substantive revision.

major comments (2)
  1. [Section IV-C, Proposition 5 (Eqs. (25), (28), (29))] The proof of Proposition 5 establishes only that det Φ(t) = det Φ0(t) + |adj{Φ0(t)}φ(t)|^2 > det Φ0(t), but the parameter error equations (11) and their explicit solutions (25) depend on Δ^2 = det^2, not on det. The step from 'larger det' to 'faster convergence' is therefore valid only if det Φ0(t) ≥ 0 (or, more generally, if |det Φ(t)| > |det Φ0(t)|), which is not established. The claim is in fact false: take m=1, φ(t) = -1, and the LTI part of H equal to 1/(p+1). Then Φ0(t) = e^{-t} - 1 < 0, and (28) gives d(t) = -1, so Φ(t) = e^{-t}. Thus det Φ0(t) < det Φ(t), yet Δ_N^2(t) = e^{-2t} < Δ_0^2(t) = (1-e^{-t})^2 for sufficiently large t. Substituting into the exact solution (25) of (11) gives \tilde θ_N(t) = \tilde θ(0) exp(-γ(1-e^{-2t})/2) and \tilde θ_0(t) = \tilde θ(0) exp(-γ∫_0^t (1-e^{-s})^2 ds); hence |\tilde θ_N(t)| > |\tilde θ_0(t)| for all sufficiently large t, and \tilde θ_N(t) does not even converge to zero. This contradicts the universal inequality in Proposition 5. A sign-compensated choice of d(t), for example d(t) = -sgn(det Φ0(t)) adj{Φ0(t)}φ(t) with an appropriate gain, might restore a form of the result, but the theorem and its proof require substantial revision.
  2. [Section VI-B, formula for \hat θ^{FTC-D}_i(t)] The simulation formula for the new finite-time estimator in Section VI-B reads \hat θ^{FTC-D}_i(t) = [\hat θ_i(t) - wD_i(t)\hat θ_i(0)]/(1-wD_i(t)). However, Proposition 7 derives the identity [1-wD_i(t)]θ_i = \hat θ_i(t) - wD_i(t)\hat θ_i(t-T_D). Substituting \hat θ_i(0) for \hat θ_i(t-T_D) is not an identity for t > T_D, so the simulated scheme is not the estimator of Proposition 7, and its claimed finite-time convergence and alertness do not follow from the theory. The implementation should use \hat θ_i(t-T_D), and the simulations must be rerun. In addition, the statement of Proposition 7 contains a typo: the right-hand side should have \hat θ_i(t), not \hat θ(t).
minor comments (7)
  1. [Section II-C] In Section II-C, the word 'propostion' should be 'proposition'.
  2. [Section V-A] In Section V-A, first paragraph, 'mutivariable' should be 'multivariable'.
  3. [Section III, Proposition 3 proof] In the proof of Proposition 3, the displayed equivalence 'Φ(k) > 0, ∀k ⇔ φ(k) ∈ PE with K ≤ \bar K' is imprecise when \bar K > K; the condition Φ(k)>0 for all k is equivalent to φ being PE with window size \bar K, not with an unspecified size K ≤ \bar K. The intended counterexample is unaffected, but the claim should be restated.
  4. [Abstract and Introduction] The abstract and introduction advertise a 'unified treatment' of continuous- and discrete-time cases, but Propositions 3, 5, and 7 are each developed for a single time domain (DT for Prop. 3, CT for Props. 5 and 7). Section VII acknowledges that some CT results remain to be derived in DT; the wording should be tempered accordingly.
  5. [Section VI-B] In Section VI-B, the simulation description says the new FTC estimate is 'computed as soon as wD_i(t) < μ_i', but it does not specify what the estimator outputs when wD_i(t) ≥ μ_i; this should be stated for reproducibility.
  6. [Equation (36)] Equation (36) is derived under the standing assumption that Δ(t-T_D)=0 for t<T_D; this assumption is mentioned in the proof but could be highlighted in the proposition statement.
  7. [Acknowledgment] In the acknowledgments, 'supported by by' should read 'supported by'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: all new claims are proven from first-principles calculations; self-citations are routine and not load-bearing.

full rationale

The paper's new contributions—the strictly-weaker-excitation DREM estimator (Prop. 3), the proposed feedforward operator giving a transient improvement claim (Prop. 5), and the finite-time estimator with alertness (Prop. 7)—are each developed by explicit algebraic manipulation in the manuscript. The PEE (11), its closed-form solution (25), Sylvester's determinant identity, and the windowed-regressor identity (19) are all derived or stated with enough content that the conclusions follow from the displayed equations, not from a prior publication's verdict. The proof of Proposition 2 is cited to the authors' earlier DREM papers, but that proposition is an elementary scalar-gradient calculation and is independent, checkable support rather than a self-referential premise. The containment of Kreisselmeier's regressor extension in the proposed operator class (Prop. 4) is a direct substitution, not a renamed prediction. There is no fitted parameter later renamed as a prediction, no uniqueness theorem imported from the authors, and no ansatz smuggled in via citation. The correctness concern raised about Proposition 5—that the determinant inequality does not control the sign of the determinant and hence det^2 may decrease—is a genuine mathematical gap in the proof, not a circularity: the claimed result is not equivalent to its inputs by construction. Therefore the circularity score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical entities are postulated. The central claims rest on standard linear algebra, LTV filtering assumptions, and the standard DREM framework from the authors' prior work; the design parameters (\bar K, γ, μ, T_D) are user choices, not fitted to data.

free parameters (4)
  • window length \bar K = integer ≥ m (chosen in Prop 3)
    Design parameter for the delay-based regressor extension; the theorems require \bar K ≥ m but no data fitting is involved.
  • gradient gain γ_i = positive constant (γ=1, γ=2 in simulations)
    DREM scalar estimator gain; affects convergence speed but not the structural claims.
  • clipping threshold μ_i = 0.98 in simulations
    Threshold in finite-time estimator; user-choice design parameter, not fitted to data.
  • sliding window T_D = 0.2 in simulations
    Memory length in alert finite-time estimator; chosen by hand for the simulation.
assumptions (5)
  • domain assumption The estimation error ε_t in LRE (1) is exponentially decaying and can be omitted (Section II).
    Standard in adaptive control; the paper does not analyze estimator robustness to non-vanishing noise.
  • domain assumption The operator H is linear and BIBO stable, so Y = H[y] = H[φ^T]θ = Φθ (Eq. (6)).
    Requires boundedness of signals and linearity; used throughout to generate scalar LREs.
  • standard math Adjugate identity adj{M}M = det{M}I_m, cited from [12] and used in Eq. (7).
    Standard linear algebra result used to derive the scalar LREs.
  • standard math Sylvester's determinant formula det(A+bc^T)=det(A)+c^T adj(A) b, used in Prop 5.
    Used to compute det{Φ} increment from the feedforward term.
  • standard math PE window monotonicity: if φ ∈ PE with window K, then it is PE for any window \bar K ≥ K (used in Prop 3).
    Consequence of Definition 1; used for implications (15) and (17).

how reviews work

0 comments
Cite this review

Pith. "Pith review of New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases." pith.science (2026). https://pith.science/paper/4E5C6NNX

@misc{pith2026190805125,
  author       = {Pith},
  title        = {Pith review of: New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4E5C6NNX}},
  note         = {Machine review of arXiv:1908.05125}
}
read the original abstract

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include: (i) a unified treatment of the continuous and the discrete-time cases; (ii) the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and (iii) an alternative estimator ensuring parameter estimation in finite-time that retains its alertness to track time-varying parameters. Simulations that illustrate our results are also presented.

Figures

Figures reproduced from arXiv: 1908.05125 by the authors.

Figure 1
Figure 1. Transients of the parameter estimation errors for dif￾ferent estimators and the control input u(t) = 15 sin(2.5t+1). 0 1 2 3 4 5 -1 0 1 2 3 4 5 Gradient DREM LTI DREM LTV (a) Parameter estimation error θ˜1(t) 0 1 2 3 4 5 -2 -1 0 1 2 3 4 Gradient DREM LTI DREM LTV (b) Parameter estimation error ˜θ2(t) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Transients of the parameter estimation errors for different estimators and the control input u(t) = 15. which is computed as soon as w D i (t) < µi . The objective of the simulation is to prove that the new FTC DREM is able to track time-varying parameters when new excitation arrives. This is in contrast with the old FTC DREM estimator that, since w(t) → 0, converges to the gradient estimator and loses its FTC alert… view at source ↗
Figure 3
Figure 3. Transients of the parameter estimates for t ∈ [0, 3] with ∆(t) ∈ P E. 10 15 20 25 30 35 40 10 12 14 16 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Transients of the parameter estimates for t ∈ [9, 40] with ∆(t) ∈ P E. effect of an additive signal in the LRE (1), to study its input￾to-state stability properties. A widely open, long-term research topic is how to deal with nonlinear parameterizations, that is, the c…
Figure 5
Figure 5. Figure 5: Transients of the parameter estimates for ∆(t) = 1 t+1 . This paper is partly supported by by Government of Russian Federation (GOSZADANIE 2.8878.2017/8.9, grant 08-08), the European Union’s Horizon 2020 Research and Innovation Programme under Grant 739551 (KIOS CoE). …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

22 extracted references · 20 canonical work pages

  1. [1]

    Skantze and A

    A.Annaswamy, F. Skantze and A. Loh, Adaptive control of c ontinuous time systems with convex/concave parametrization, Automatica, vol. 34, no. 1, pp. 33-49, 1998

    work page 1998

  2. [2]

    Aranovskiy, A

    S. Aranovskiy, A. Bobtsov, R. Ortega and A. Pyrkin, Perfo rmance enhancement of parameter estimators via dynamic regressor extension and mixing, IEEE Trans. Automatic Control , vol. 62, no 7, pp.3546- 3550, 2017

    work page 2017

  3. [3]

    Astolfi, D

    A. Astolfi, D. Karagiannis and R. Ortega, Nonlinear and Adaptive Control with Applications, Springer-V erlag, Berlin, Communications and Control Engineering, 2008

    2008

  4. [4]

    Belov, S

    A. Belov, S. Aranovskiy, R. Ortega, N. Barabanov and A. Bo btsov, Enhanced parameter convergence for linear systems identifi cation: The DREM approach, 2018 European Control Conference , Limassol, Cyprus, 12-15/06, 2018. (To appear in Int. J. on Adaptive Control and Signal Processing)

    work page 2018

  5. [5]

    Belov, R

    A. Belov, R. Ortega and A. Bobtsov, Guaranteed performan ce adaptive identification scheme of discrete-dime systems using dynam ic regressor extension and mixing, 18th IF AC Symposium on System Identification, (SYSID 2018) , Stockholm, Sweden, July 9-11, 2018

    work page 2018

  6. [6]

    N. Cho, H. Shin, Y . Kim and A. Tsourdos, Composite MRAC wit h parameter convergence under finite excitation, IEEE Trans. Automatic Control, vol. 63, no. 3, pp. 811-818, 2018

    work page 2018

  7. [7]

    Chowdhary, T

    G. Chowdhary, T. Y ucelen, M. Mhlegg and E. Johnson, Concu rrent learning adaptive control of linear systems with exponenti ally convergent bounds, Int. J. on Adaptive Control and Signal Processing , vol. 27, no. 4, pp. 280-301, 2013

    work page 2013

  8. [8]

    Gerasimov, R

    D. Gerasimov, R. Ortega and V . Nikiforov, Adaptive contr ol of mul- tivariable systems with reduced knowledge of high frequenc y gain: Application of dynamic regressor extension and mixing esti mators, 18th IF AC Symposium on System Identification, (SYSID 2018) , Stockholm, Sweden, July 9-11, 2018

    work page 2018

Show all 22 references
  1. [9]

    Goodwin and K.S

    G.C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control , Prentice-Hall, 1984

    1984

  2. [10]

    Ioannou and J

    P . Ioannou and J. Sun, Robust Adaptive Control, Prentice–Hall, NJ, 1996

    1996

  3. [11]

    Kreisselmeier, Adaptive observers with exponentia l rate of conver- gence, IEEE Trans

    G. Kreisselmeier, Adaptive observers with exponentia l rate of conver- gence, IEEE Trans. Automatic Control , vol. 22, no. 1, pp. 2-8, 1977

    1977

  4. [12]

    Lancaster and M

    P . Lancaster and M. Tismenetsky, The Theory of Matrices , Academic Press, NY , 1985

    1985

  5. [13]

    Lion, Rapid identification of linear and nonlinear systems, AIAA Journal, vol

    P .M. Lion, Rapid identification of linear and nonlinear systems, AIAA Journal, vol. 5, pp. 1835-1842, 1967

    1967

  6. [14]

    X. Liu, R. Ortega, H. Su and J. Chu. Immersion and invaria nce adaptive control of nonlinearly parameterized nonlinear systems, IEEE Trans. Automatic Control, vol. 55, no. 9, pp. 2209-2214, 2010

    2010

  7. [15]

    X. Liu, R. Ortega, H. Su and J. Chu, On adaptive control of nonlinearly parameterized nonlinear systems: towards a constructive p rocedure, Systems and Control Letters , vol. 10, pp. 36-43, 2011

    2011

  8. [16]

    Ljung, System Identification: Theory for the User , Prentice Hall, New Jersey, 1987

    L. Ljung, System Identification: Theory for the User , Prentice Hall, New Jersey, 1987

    1987

  9. [17]

    Narendra and A

    K. Narendra and A. Annaswamy, Stable Adaptive Systems, Prentice Hall, New Jersey, 1989

    1989

  10. [18]

    Ortega, L Praly, S

    R. Ortega, L Praly, S. Aranovskiy, B Yi and W. Zhang, On dy namic regressor extension and mixing parameter estimators: Two L uenberger observers interpretations, Automatica, vol. 95, pp. 548-551, 2018

    2018

  11. [19]

    Ortega, V

    R. Ortega, V . Nikiforov and D. Gerasimov, On modified par ameter estimators for identification and adaptive control: A unifie d framework and some new schemes, ITMO Int. Report , 2018

    2018

  12. [20]

    Roy and S

    S.B. Roy and S. Bhasin and I.N. Kar, Combined MRAC for unk nown MIMO LTI systems with parameter convergence, IEEE Transactions on Automatic Control, vol. 63, no. 1, pp. 283-290, 2018,

    2018

  13. [21]

    Sastry and M

    S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Prentice-Hall, New Jersey, 1989

    1989

  14. [22]

    B. Yi, R. Ortega, H. Siguerdidjane, J. Machado and W. Zha ng, On generation of virtual outputs via signal injection: Applic ation to observer design for electromechanical systems, LSS-Supelec Int. Report , 2018. 8

    2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.