Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals

Carlo Scholz; Johannes K\"ohler; Melanie Zeilinger

REVIEW 3 major objections 6 minor 30 references

Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals

T0 review · 3 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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

Pith's one-line read The paper proves that a reduced-order model, paired with a scalar filter-driven error bound, can guarantee constraint satisfaction in model predictive control.

desk verdict A genuine improvement in ROM-based MPC error bounds, but the filtered-peak LMI smuggles in a DC-gain matching condition that needs to be stated. read the letter →

arxiv 2511.03002 v3 pith:PEX63ND5 submitted 2025-11-04 eess.SY cs.SYmath.OC

Johannes Köhler , Carlo Scholz , Melanie Zeilinger This is my paper · ORCID

classification eess.SYcs.SYmath.OC MSC 93C0593D0993B40

keywords modelpredictivecontrolreduced-ordermodelserror-boundingsystempeak-to-peakgainfilteredsignalsrobustconstraintsatisfactionlinearmatrixinequalitieslarge-scalesystems

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

Model-predictive control of large linear systems normally requires solving a high-dimensional optimal control problem online. The paper shows that a small reduced-order model can run the MPC safely if it is accompanied by a scalar 'error-bounding system' that, driven by a filtered version of the predicted trajectory, provides a pointwise upper bound on the difference between the reduced-order output and the full-order output. This bound is computed offline via a peak-to-peak gain LMI, and online it is used to tighten constraints and to bound the cost. On a 100-dimensional mass-spring-damper example, the method reduces conservatism by over four orders of magnitude compared with existing ROM-based MPC bounds, and it enables operation close to the constraint boundary.

What carries the argument

Peak-to-peak analysis of filtered signals: a stable linear dynamic filter Ψ (state ψ, output rψ) transforms the lumped error input r into a filtered signal; the augmented error-filter dynamics (16) are analyzed through the LMI (17), which minimizes the output-to-output gain γχ. The associated Lyapunov function Vχ and decay rate λχ yield the scalar error-bounding system (18), whose trajectory δχ(t) gives the pointwise bound (19) and hence the implementable bound (22). The ROM is a standard Petrov-Galerkin projection with residual operator I − V W^T, and the filter is a design choice that can encode frequency-domain knowledge about where the ROM is accurate.

What would settle it

Solve the LMI (17) for a chosen filter and ROM on a system where the ROM's DC gain differs from the full-order system's DC gain on the filtered channels. If the LMI is feasible yet a worst-case simulation violates ∥zr(t) − z(t)∥ ≤ δz(t), then the peak-to-peak bound (22) fails; if the LMI is infeasible, the proposed scheme cannot be applied at all.

Watch

Extended reading notes

Core claim

The central claim (Theorem 1) is that any feasible input of the reduced-order optimal control problem (24) is feasible for the original full-order constrained optimal control problem (4), and its cost is no larger than the reduced-order cost. This is carried by Lemma 1: the scalar system (21) predicts δz(t) with ∥zr(t) − z(t)∥ ≤ δz(t) for all admissible disturbances, provided the filter-based peak-to-peak analysis in (17) is feasible. The novel step is the use of a dynamic filter Ψ on the lumped input so that the error bound reflects the frequency content of the trajectory. A high-pass filter makes the bound vanish at steady state, which is why the numerical example reaches zero conservatism

Load-bearing premise

The entire result hinges on the offline LMI (17) being feasible for the chosen filter, which the paper simply supposes; with a high-pass filter this requires the reduced-order model's steady-state gain to match the full-order system on the filtered channels, a condition that is neither stated nor verified.

Editorial extensions

If this is right

The online MPC complexity depends on the ROM dimension nr plus the filter dimension nψ plus one scalar, not on the full order nf, enabling real-time control of large-scale systems.
Every feasible solution of the reduced-order problem (24) satisfies the full-order constraints for all admissible disturbances and yields a cost no larger than the reduced-order cost (Theorem 1).
Because the error bound depends on the optimized trajectory, the optimizer inherently favors inputs that keep the prediction error small, allowing tight operation near constraints.
The high-pass filter choice makes the error bound decay to zero at steady state, eliminating the conservative offset that uniform bounds retain even at equilibrium.
A receding-horizon implementation can be obtained by adapting standard terminal conditions from the ROM-based MPC literature, as noted in Remark 2.

Reading between the lines

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

The filter is chosen heuristically; a joint offline optimization of the ROM and the filter could further shrink the error bound and is not explored in the paper.
The feasibility of the offline LMI (17) is assumed, but for high-pass filters it implicitly requires the ROM's steady-state gain to match the full-order system on the filtered channels; this condition is not verified and should be checked before deployment.
The IQC reformulation in Appendix A suggests a unified framework where filters describe both model error and peak-to-peak weighting; unifying these two filter roles could lower the LMI dimension and scale to even larger systems.
The method is presented for linear continuous-time systems, but the same filtered-peak-to-peak machinery could likely be adapted to discrete-time or mildly nonlinear ROMs, though the paper does not claim this.

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.

Desk Editor's Note

read the letter

Short version: this is a solid paper and a real step forward for ROM-based MPC. The filtered peak-to-peak error-bounding system is new relative to the scalar, hand-tuned bounds in [18] and the Lipschitz-based ones in [19], and the main theorem is conditionally sound. What you should check before building on it is the feasibility of LMI (17): with a high-pass filter it implicitly requires exact DC-gain matching, and the paper neither states nor verifies that.

The core idea is clean. They write the full-order error dynamics as a linear system driven by the ROM state, input, and disturbance, then use a peak-to-peak LMI to get a scalar bounding ODE. The generalization in Sec. V replaces the raw input r by a filtered signal r_psi, so the bound can be small when the excitation is smooth—exactly where ROMs are usually accurate. I checked the Schur complements in Props. 2 and 3 and the proof of Theorem 1; they go through. The qualitative comparison to IQC-based methods in Appendix A is honest: their filtered norm is not a special case of IQC filtering, which is worth saying.

The soft spots are real but addressable. Problem (17) is 'supposed' feasible; feasibility is not automatic. For a high-pass filter, r_psi tends to zero at constant inputs, so the dissipation inequality forces the steady-state error to zero. That means the ROM must exactly match the full-order DC gain on the filtered channels. The example apparently satisfies this, but the paper gives no design rule and doesn't even state the condition. Its absence matters because the headline four-orders-of-magnitude result rests on this filter working. Relatedly, the filter itself (frequency, normalization) is chosen heuristically, and the conservatism comparison is done on a single 100-dimensional example. For a methods paper that's acceptable, but both points should be made explicit and at least one more example would help.

I'd send this to peer review. The conditional guarantee is not a fatal flaw, but the authors need to characterize feasibility of (17) or give a verifiable procedure for choosing Psi, and state the DC-gain condition. If that gets fixed, the contribution is solid and useful.

Referee Report

3 major / 6 minor

Summary. The paper proposes a ROM-based MPC scheme for stable linear continuous-time systems with hard input/output constraints and bounded disturbances. The full-order system is decomposed into a Petrov–Galerkin ROM and an error dynamics driven by the ROM state and input. The authors derive a scalar error-bounding system whose constants are obtained offline from peak-to-peak LMIs, first with the raw excitation and then with a dynamically filtered excitation. This bound is embedded in a reduced-order optimal control problem with tightened constraints, and Theorem 1 states that any feasible input of this problem is feasible for the full-order robust optimal control problem with a guaranteed cost bound. The method is illustrated on a 100-dimensional mass–spring–damper system, reporting a reduction in conservatism of four orders of magnitude relative to existing ROM-based approaches.

Significance. If the result holds, the paper is a valuable contribution to ROM-based MPC: it provides pointwise, input-dependent prediction error bounds rather than uniform bounds, it replaces hand-tuned error-bounding constants with LMI-based optimization, and it demonstrates a filter extension that can make the bound vanish at steady state. The theoretical structure is clear and the proofs are largely standard. The paper also ships open-source code, which supports reproducibility. The main reservation is that the headline improvement relies on feasibility of the filtered LMI (17), and the paper does not analyze the structural condition that this feasibility implies for high-pass filters; as a result, the general applicability of the approach is not fully established.

major comments (3)

[Sec. V, Eq. (17); Lemma 1 and Theorem 1] Problem (17) is only 'supposed' to be feasible, but the paper does not analyze when this is true. For the high-pass filter used in Sec. VIII, rψ(t) tends to 0 for any constant input r. At the resulting steady state, the dissipation inequality from (17b) gives λχVχ(χ∞) ≤ 0, so Vχ(χ∞)=0; the output LMI (17c) then implies C_zχ∞=0, i.e., the steady-state error ze vanishes for all constant inputs. Feasibility of (17) with a high-pass filter therefore entails exact DC-gain matching between the ROM and the full-order model on the filtered channels. This condition is neither stated nor verified, and no design rule is given to enforce it; the filter is chosen heuristically in Sec. VIII. Since the Peak-filter result of Fig. 4 and Theorem 1 both depend on this LMI being feasible, the general applicability of the method is not established. Please state the feasibility condition explicitly, explain h
[Sec. V and Sec. VIII, filter design] The dynamic filter Ψ is a key enabler of the reported improvement, but its selection is entirely heuristic: a first-order high-pass filter with nψ=nr+nu is chosen, and the normalization and frequency are said to be 'chosen heuristically'. The paper claims a systematic framework, yet gives no guidance on choosing Ψ or on how the result depends on that choice. A sensitivity study or an optimization-based filter selection would substantially strengthen the contribution. Without it, the four-orders-of-magnitude improvement cannot be separated from a favorable filter choice.
[Eq. (15) and Lemma 1] The printed condition (15) is unclear and, as written, only states that the first nw components of rψ equal w. The proof of Lemma 1, however, uses the stronger structural identity rψ(t)=¯rψ(t)+[I,0]^T w(t), which also requires that the remaining components of rψ be independent of w. The latter property is needed for the bound ∥rψ∥² ≤ ∥¯rψ∥²+¯w² used in (21c). Please rewrite (15) in clear component form and include the full structural argument in the proof of Lemma 1.

minor comments (6)

[Abstract] Typo: 'an (iii)' should be 'and (iii)'.
[Sec. V, Eq. (15)] The matrix expression in (15) is garbled in the typeset version; please fix the formatting and define all blocks explicitly.
[Sec. VII] Typo: 'polyotpic' should be 'polytopic'.
[Sec. VIII] The numerical example considers no disturbances (w=0). The theoretical guarantee covers disturbances, but this aspect is not demonstrated. A small disturbance case would strengthen the validation.
[Sec. VIII] Minor grammar issue: 'the large difference is primarily due the choice' should be 'due to the choice'.
[Appendix A] Typo: 'We except that' should be 'We expect that'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the error bound is derived from external LMIs and the proof is self-contained relative to its stated assumptions.

full rationale

The central claim is a genuine derivation rather than a circular restatement. The scalar error-bounding system (18) and its implementable counterpart (21) are obtained from the peak-to-peak LMI conditions (10) and (17), which are attributed to the external lecture notes [28] (Scherer-Weiland). The constants lambda, gamma are chosen by solving the LMIs offline; they are not fitted to the example or to the bound they later certify. Proposition 2 and Proposition 3 establish the key inequality via the dissipation inequality (13) and a comparison argument, and Lemma 1 then proves ||zr(t)-z(t)|| <= delta_z(t) without assuming the desired bound as an input. Theorem 1 is explicitly conditional: the paper states 'we suppose that Problem (17) admits a feasible solution' and similarly assumes feasibility of Problem (24). This is an unverified regularity condition, not a circular reduction; in particular, feasibility of (17) is not equivalent to the statement of the bound. The numerical comparison evaluates the bounds along the optimized trajectory, which is a legitimate benchmark for bound tightness and not a fitted prediction. Self-citations such as [19], [23], and [26] are used for context, comparison, or an appendix adaptation and are not load-bearing for the main theorem; the central LMI is from external literature. The high-pass-filter DC-gain feasibility caveat is a correctness concern about when (17) is feasible, not evidence that the derivation reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The formal derivation is self-contained given standard LMI machinery, but it introduces no new physical entities. Its practical guarantees depend on a handful of design choices (ROM, filter, line-search grid) and on feasibility assumptions that are not fully characterized.

free parameters (3)

Filter dynamics Ψ (Aψ,Bψ,Cψ,Dψ) = First-order high-pass with 'heuristically chosen' normalization and frequency (Sec. VIII)
The conservatism reduction in the numerical example depends critically on this design choice; no systematic filter synthesis is provided.
ROM projectors (W,V) = 8th-order ROM: 2D lumped model + 6 slowest eigenmodes (Sec. VIII)
The ROM is a design choice; the error bound depends on it, but any Petrov-Galerkin ROM is admissible.
Line-search grid for λχ = 10 equally spaced values (Sec. VIII)
The offline SDP is solved for a fixed grid of λχ; the bound quality depends on the grid.

assumptions (5)

domain assumption Full-order system (A,B,E,C) and initial condition x0 are perfectly known (Sec. II)
Stated simplifying condition; the error bound covers only ROM mismatch, not model uncertainty.
domain assumption A is Hurwitz (open-loop stable) (Sec. II)
Feasibility of peak-to-peak LMI and bounded error dynamics rely on stability.
ad hoc to paper Problem (17) admits a feasible solution (Sec. V)
Stated as a supposition, not proven; the formal MPC guarantees depend on it. With a high-pass filter, feasibility implicitly requires exact DC-gain matching of the ROM.
domain assumption Filter pass-through structure (15) is realizable
The implementable bound (21c) assumes the disturbance w(t) appears as a dedicated orthogonal component of rψ(t).
standard math LMI (10)/(17) from [28, Prop. 3.16] correctly characterize peak-to-peak gains
Standard robust control result, referenced to an external textbook.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals." pith.science (2026). https://pith.science/paper/PEX63ND5

@misc{pith2026251103002,
  author       = {Pith},
  title        = {Pith review of: Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PEX63ND5}},
  note         = {Machine review of arXiv:2511.03002}
}

read the original abstract

We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to achieve computational tractability with robust constraint satisfaction. Our key contribution is a method to obtain guaranteed bounds on the predicted outputs of the full-order system by predicting a (scalar) error-bounding system alongside the ROM. This bound is then used to formulate a robust ROM-based MPC that guarantees constraint satisfaction and robust performance. Our method is developed step-by-step by (i) analysing the error, (ii) bounding the peak-to-peak gain, an (iii) using filtered signals. We demonstrate our method on a 100-dimensional mass-spring-damper system, achieving over four orders of magnitude reduction in conservatism relative to existing approaches.

Figures

Figures reproduced from arXiv: 2511.03002 by the authors.

**Figure 1.** Numerical example: chain of N = 50 masses connected by spring and damper elements with first position z and control input u. 0 5 10 15 20 0 0.5 1 Constraint ROM-prediction Full-order simulation [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 3.** Proposed robust ROM-based MPC (24): Full-order simu [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 2.** Na¨ıve ROM-based MPC: Trajectory optimized with nom [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Comparison of prediction error bounds of ROM. The das [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 1 linked inside Pith

[18]

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems,

M. Loehning, M. Reble, J. Hasenauer, S. Y u, and F. Allgoe wer, “Model predictive control using reduced order models: Guaranteed stability for constrained linear systems,” Journal of Process Control , vol. 24, no. 11, pp. 1647–1659, 2014

2014
[19]

Robust nonlinear redu ced-order model predictive control,

J. I. Alora, L. A. Pabon, J. K¨ ohler, M. Cenedese, E. Schm erling, M. N. Zeilinger, G. Haller, and M. Pavone, “Robust nonlinear redu ced-order model predictive control,” in Proc. 62nd IEEE Conference on Decision and Control (CDC) . IEEE, 2023, pp. 4798–4805

2023
[1]

J. B. Rawlings, D. Q. Mayne, and M. Diehl, Model Predictive Control: Theory, Computation, and Design . Nob Hill Publishing, 2017

2017
[2]

Recen t advances in quadratic programming algorithms for nonlinear model pr edictive control,

D. Kouzoupis, G. Frison, A. Zanelli, and M. Diehl, “Recen t advances in quadratic programming algorithms for nonlinear model pr edictive control,” Vietnam J. Mathematics , vol. 46, no. 4, pp. 863–882, 2018

2018
[3]

A survey of industrial model predictive control technology,

S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control engineering practice , vol. 11, no. 7, pp. 733–764, 2003

2003
[4]

Model predictiv e control of legged and humanoid robots: models and algorithms,

S. Katayama, M. Murooka, and Y . Tazaki, “Model predictiv e control of legged and humanoid robots: models and algorithms,” Advanced Robotics, vol. 37, no. 5, pp. 298–315, 2023

2023
[5]

Latest advances of model predictive control in electrical drives—part i: Basic concepts and advanced strategies,

J. Rodriguez, C. Garcia, A. Mora, F. Flores-Bahamonde, P . Acuna, M. Novak, Y . Zhang, L. Tarisciotti, S. A. Davari, Z. Zhang et al. , “Latest advances of model predictive control in electrical drives—part i: Basic concepts and advanced strategies,” IEEE Transactions on Power Electronics, vol. 37, no. 4, pp. 3927–3942, 2021

2021
[6]

An overview of approximation methods fo r large- scale dynamical systems,

A. C. Antoulas, “An overview of approximation methods fo r large- scale dynamical systems,” Annual reviews in Control , vol. 29, no. 2, pp. 181–190, 2005

2005

Show all 30 references

[7]

Identiﬁcation and model pred ictive control of an industrial glass-feeder,

L. Huisman and S. Weiland, “Identiﬁcation and model pred ictive control of an industrial glass-feeder,” IF AC Proceedings V olumes, vol. 36, no. 16, pp. 1645–1649, 2003

2003
[8]

Model reducti on using proper orthogonal decomposition and predictive control of distributed reactor system,

A. Marquez, J. J. E. Oviedo, and D. Odloak, “Model reducti on using proper orthogonal decomposition and predictive control of distributed reactor system,” Journal of Control Science and Engineering , vol. 2013, no. 1, p. 763165, 2013

2013
[9]

Soft robot opt imal control via reduced order ﬁnite element models,

S. Tonkens, J. Lorenzetti, and M. Pavone, “Soft robot opt imal control via reduced order ﬁnite element models,” in Proc. IEEE International Conference on Robotics and Automation (ICRA) , 2021, pp. 12 010– 12 016

2021
[10]

Hierarchic al reduced- order model predictive control for robust locomotion on hum anoid robots,

A. B. Ghansah, S. A. Esteban, and A. D. Ames, “Hierarchic al reduced- order model predictive control for robust locomotion on hum anoid robots,” in Proc. IEEE-RAS 24th International Conference on Hu- manoid Robots (Humanoids) , 2025, pp. 1–8

2025
[11]

Online model order re duction of linear systems via ( γ, δ)-similarity,

S. Bajaj, C. L. Beck, and V . Gupta, “Online model order re duction of linear systems via ( γ, δ)-similarity,” arXiv preprint arXiv:2504.10437 , 2025

2025 arXiv
[12]

A posteriori error estimation for DEIM reduced nonlinear dynamical systems,

D. Wirtz, D. C. Sorensen, and B. Haasdonk, “A posteriori error estimation for DEIM reduced nonlinear dynamical systems,” SIAM Journal on Scientiﬁc Computing, vol. 36, no. 2, pp. A311–A338, 2014

2014
[13]

Kouvaritakis and M

B. Kouvaritakis and M. Cannon, Model predictive control . Springer, 2016

2016
[14]

Constra ined model predictive control based on reduced-order models,

P . Sopasakis, D. Bernardini, and A. Bemporad, “Constra ined model predictive control based on reduced-order models,” in Proc. 52nd IEEE Conference on Decision and Control . IEEE, 2013, pp. 7071–7076

2013
[15]

Robust output feedback mod el predictive control using reduced order models,

M. K¨ ogel and R. Findeisen, “Robust output feedback mod el predictive control using reduced order models,” IF AC-PapersOnLine, vol. 48, no. 8, pp. 1008–1014, 2015

2015
[16]

Linear reduced-order model predictive control,

J. Lorenzetti, A. McClellan, C. Farhat, and M. Pavone, “ Linear reduced-order model predictive control,” IEEE Transactions on Au- tomatic Control, vol. 67, no. 11, pp. 5980–5995, 2022

2022
[17]

Tube-based robust MPC for two-t imescale systems using reduced-order models,

W. Wang and J. P . Koeln, “Tube-based robust MPC for two-t imescale systems using reduced-order models,” IEEE Control Systems Letters , vol. 7, pp. 799–804, 2022

2022
[20]

Zhou and J

K. Zhou and J. C. Doyle, Essentials of robust control . Prentice hall Upper Saddle River, NJ, 1998, vol. 104

1998
[21]

Getting robustness against u nstructured uncertainty: a tube-based MPC approach,

P . Falugi and D. Q. Mayne, “Getting robustness against u nstructured uncertainty: a tube-based MPC approach,” IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1290–1295, 2014

2014
[22]

Robust output -feedback model predictive control for systems with unstructured unc ertainty,

C. Løvaas, M. M. Seron, and G. C. Goodwin, “Robust output -feedback model predictive control for systems with unstructured unc ertainty,” Automatica, vol. 44, no. 8, pp. 1933–1943, 2008

1933
[23]

Model predictive control for linear uncertain systems using inte gral quadratic constraints,

L. Schwenkel, J. K¨ ohler, M. A. M¨ uller, and F. Allg¨ owe r, “Model predictive control for linear uncertain systems using inte gral quadratic constraints,” IEEE Transactions on Automatic Control , vol. 68, no. 1, pp. 355–368, 2022

2022
[24]

Output-feedback model predictive control under d ynamic un- certainties using integral quadratic constraints,

——, “Output-feedback model predictive control under d ynamic un- certainties using integral quadratic constraints,” in Proc. 64th IEEE Conf. Decision and Control (CDC) , 2025

2025
[25]

Dissipativity and integral quadratic c onstraints: Tai- lored computational robustness tests for complex intercon nections,

C. W. Scherer, “Dissipativity and integral quadratic c onstraints: Tai- lored computational robustness tests for complex intercon nections,” IEEE Control Systems Magazine , vol. 42, no. 3, pp. 115–139, 2022

2022
[26]

Robust peak-to-peak gain analysis using integral quadratic const raints,

L. Schwenkel, J. K¨ ohler, M. A. M¨ uller, and F. Allg¨ owe r, “Robust peak-to-peak gain analysis using integral quadratic const raints,” IF AC- PapersOnLine, vol. 56, no. 2, pp. 11 564–11 569, 2023

2023
[27]

Multi-objective robust controller synthesis with integr al quadratic constraints in discrete-time,

L. Schwenkel, J. K¨ ohler, M. A. M¨ uller, C. W. Scherer, and F. Allg¨ ower, “Multi-objective robust controller synthesis with integr al quadratic constraints in discrete-time,” International Journal of Robust and Nonlinear Control, 2025

2025
[28]

Linear matrix inequalities in control,

C. Scherer and S. Weiland, “Linear matrix inequalities in control,” Lecture Notes, Delft University, The Netherlands , vol. 3, 2000

2000
[29]

Efﬁciently computing the cyclic output-to-output gain,

D. Arnstr¨ om and A. M. Teixeira, “Efﬁciently computing the cyclic output-to-output gain,” arXiv preprint arXiv:2509.16665 , 2025

2025
[30]

Exponential decay rate conditions for uncertain linear systems using integral quadratic constraints,

B. Hu and P . Seiler, “Exponential decay rate conditions for uncertain linear systems using integral quadratic constraints,” IEEE Transactions on Automatic Control , vol. 61, no. 11, pp. 3631–3637, 2016. APPENDIX A. IQC-based peak-to-peak reachability analysis In the following...

2016

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [18]

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems,

M. Loehning, M. Reble, J. Hasenauer, S. Y u, and F. Allgoe wer, “Model predictive control using reduced order models: Guaranteed stability for constrained linear systems,” Journal of Process Control , vol. 24, no. 11, pp. 1647–1659, 2014

2014

[2] [19]

Robust nonlinear redu ced-order model predictive control,

J. I. Alora, L. A. Pabon, J. K¨ ohler, M. Cenedese, E. Schm erling, M. N. Zeilinger, G. Haller, and M. Pavone, “Robust nonlinear redu ced-order model predictive control,” in Proc. 62nd IEEE Conference on Decision and Control (CDC) . IEEE, 2023, pp. 4798–4805

2023

[3] [1]

J. B. Rawlings, D. Q. Mayne, and M. Diehl, Model Predictive Control: Theory, Computation, and Design . Nob Hill Publishing, 2017

2017

[4] [2]

Recen t advances in quadratic programming algorithms for nonlinear model pr edictive control,

D. Kouzoupis, G. Frison, A. Zanelli, and M. Diehl, “Recen t advances in quadratic programming algorithms for nonlinear model pr edictive control,” Vietnam J. Mathematics , vol. 46, no. 4, pp. 863–882, 2018

2018

[5] [3]

A survey of industrial model predictive control technology,

S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control engineering practice , vol. 11, no. 7, pp. 733–764, 2003

2003

[6] [4]

Model predictiv e control of legged and humanoid robots: models and algorithms,

S. Katayama, M. Murooka, and Y . Tazaki, “Model predictiv e control of legged and humanoid robots: models and algorithms,” Advanced Robotics, vol. 37, no. 5, pp. 298–315, 2023

2023

[7] [5]

Latest advances of model predictive control in electrical drives—part i: Basic concepts and advanced strategies,

J. Rodriguez, C. Garcia, A. Mora, F. Flores-Bahamonde, P . Acuna, M. Novak, Y . Zhang, L. Tarisciotti, S. A. Davari, Z. Zhang et al. , “Latest advances of model predictive control in electrical drives—part i: Basic concepts and advanced strategies,” IEEE Transactions on Power Electronics, vol. 37, no. 4, pp. 3927–3942, 2021

2021

[8] [6]

An overview of approximation methods fo r large- scale dynamical systems,

A. C. Antoulas, “An overview of approximation methods fo r large- scale dynamical systems,” Annual reviews in Control , vol. 29, no. 2, pp. 181–190, 2005

2005