On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers

Dimitri Peaucelle; Hibiki Gyotoku; Sophie Tarbouriech; Tsuyoshi Yuno; Victor Magron; Yoshio Ebihara

REVIEW 2 major objections 5 minor 2 cited by

On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read A rank-one solution of the dual LMI proves the feedback system is not absolutely stable, by exposing a slope-restricted nonlinearity with a nonzero equilibrium.

desk verdict A sound and genuinely constructive dual-LMI instability certificate, but the advertised bridge from primal infeasibility to a rank-one dual solution remains unproven. read the letter →

arxiv 2411.14339 v1 pith:7WXBQBKK submitted 2024-11-21 math.OC

Hibiki Gyotoku , Tsuyoshi Yuno , Yoshio Ebihara , Victor Magron , Dimitri Peaucelle , Sophie Tarbouriech This is my paper · ORCID

classification math.OC MSC 93D1093D0590C22

keywords absolutestabilityintegralquadraticconstraintsO'Shea-Zames-Falbmultipliersslope-restrictednonlinearitiesduallinearmatrixinequalitiesrank-onesolutiondestabilizingnonlinearitynonzeroequilibrium

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 addresses a blind spot in absolute-stability analysis: the standard certificates built from integral quadratic constraints (IQC) and solved as linear matrix inequalities (LMIs) are only sufficient, so when the LMI is infeasible nothing is known. The authors derive the dual LMI and show that if it has a feasible solution of rank one, then the system is definitely not absolutely stable. In that case the solution directly yields a destabilizing nonlinearity inside the prescribed slope class and a nonzero equilibrium point of the closed loop. This turns a failed numerical certificate into a constructive instability proof.

What carries the argument

The engine is the dual LMI (11), obtained by Lagrange duality from the primal certificate built on static O'Shea-Zames-Falb multipliers, the multiplier matrices that encode the input-output slope constraints of the nonlinearity inside the IQC framework. A feasible rank-one solution $H=[h_1;h_2][h_1;h_2]^T$ does three things at once. The first equality constraint becomes $\mathrm{He}\{(Ah_1+Bh_2)h_1^T\}=0$, and since $h_1\neq0$ this forces $Ah_1+Bh_2=0$, making $h_1$ a zero of the vector field. The second constraint rewrites as $w^*(z^*-w^*)^T=1_m f^T+g1_m^T+X$; because $f,g\ge0$ and $X$ is a zero-diagonal $Z$-matrix, this identity enforces the pointwise slope and sector conditions that guarantee an interpolating function in $\mathrm{slope}[0,1]$. The paper's piecewise-linear construction makes that interpolating function explicit.

What would settle it

A reader could solve the dual LMI (11) for a plant with $A$ Hurwitz, $\|D\|<1$, and an infeasible primal LMI (10), then check whether every feasible $H$ has rank at least two; a system of that kind that is nevertheless absolutely stable would show the certificate does not detect all instabilities. A more direct check is to take any rank-one dual solution, build $\phi_{wc}$ by the paper's piecewise-linear rule, and simulate from $x(0)=h_1$: the claim predicts the state stays exactly at $h_1$ and the constructed map lies in $\mathrm{slope}[0,1]$.

Watch

Extended reading notes

Core claim

The central discovery is Theorem 1 (and its odd-symmetry counterpart, Theorem 2). For slope-restricted nonlinearities in $[0,1]$ with $\|D\|<1$, suppose the dual LMI (11) has a rank-one solution $H=[h_1;h_2][h_1;h_2]^T$. Then $h_1\neq0$, and the points $z^*=Ch_1+Dh_2$, $w^*=h_2$ admit a function $\phi_{wc}$ in $\mathrm{slope}[0,1]$ with $\phi_{wc}(z^*_i)=w^*_i$ for each channel. With $\Phi_{wc}=\mathrm{diag}_m(\phi_{wc})$, the closed loop satisfies $x(t)=h_1$, $z(t)=z^*$, $w(t)=w^*$ for all $t\ge0$ from $x(0)=h_1$, so $h_1$ is a nonzero equilibrium and the system is not absolutely stable. The rank-one hypothesis is what converts the dual variables into a concrete state and a concrete nonlinearity.

Load-bearing premise

The theorems assume the dual LMI has a feasible solution of rank exactly one; the paper does not characterize when such a solution exists, and only two numerical examples exhibit it.

Editorial extensions

If this is right

If the dual LMI (11) is feasible with a rank-one solution, the primal OZF/IQC LMI is necessarily infeasible, so the rank-one dual certificate is a direct witness that the sufficient condition has failed.
The extracted nonlinearity $\phi_{wc}$ is an explicit destabilizing member of the assumed slope-restricted class, so the instability is witnessed by a concrete object rather than by the absence of a certificate.
The vector $h_1$ gives the exact nonzero equilibrium location, allowing direct simulation-based verification of the instability claim.
Theorem 2 provides the same constructive certificate when the nonlinearity is also required to be odd, using doubly dominant multipliers in the dual LMI (19).
In the two numerical examples, trajectories from other initial states converge to the origin while the trajectory from $h_1$ stays fixed, confirming that the certificate identifies a genuine global-stability failure.

Reading between the lines

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

If rank-one feasible solutions were typical whenever the primal LMI is infeasible, the OZF/IQC condition would become a necessary and sufficient test for absolute stability within the slope class; the paper only proves the one-way implication and gives no genericity result.
The same dual-extraction scheme could be applied to other multiplier families, such as the idempotent-nonlinearity multipliers the paper lists as future work, with the open question being whether the rank-one condition survives those multiplier sets.
One can turn the result into a screening algorithm: solve the dual semidefinite program, compute the minimum-rank feasible $H$, and if the minimum is one, output $\phi_{wc}$ and $h_1$ as an instability certificate. Whether the minimum rank is generically one is a testable numerical question.

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

Colleague,

The paper is worth a look. The genuinely new thing is a constructive instability certificate: if the dual of the OZF LMI has a rank-one feasible solution, the authors explicitly build a slope-[0,1] nonlinearity and a nonzero equilibrium for the closed loop, so the system is not absolutely stable. The odd-slope variant is a separate theorem with a more delicate interpolation argument. The proofs are careful, and the numerical examples actually exhibit the rank-one solution and the constructed equilibrium. This extends their earlier ReLU-specific dual construction to static OZF multipliers, which is a natural step but not a routine one.

Credit where it is due: the key inequalities (13)-(14) and (22)-(26) are doing real work, and the equilibrium argument from He{(Ah1+Bh2)h1^T}=0 with h1 nonzero is neat. The paper is also honest that the rank condition is a hypothesis.

The soft spots, in order. First, the rank-one condition is not derived from primal infeasibility. The abstract and introduction advertise a way to conclude non-absolute-stability when the LMI is infeasible, but the theorems actually prove a conditional statement. The dual certificate from LMI alternatives can have rank greater than one, and the paper gives no extreme-ray or rank-reduction argument to show that a rank-one solution exists whenever the primal fails. The two examples show it can happen, not that it typically does. This does not invalidate the theorems, but it is a real gap between the stated motivation and the result. Second, the extraction theorems are specialized to slope [0,1] and ||D||<1; the general mu,nu setup is dualized but the rank-one construction only runs in the normalized case. That is a scope limitation, not an error. Third, the numerical section has no solver details, tolerance thresholds, or code, so the rank-one declarations are not independently reproducible from the manuscript alone. Minor: the primal-dual equivalence is cited rather than proved, which is acceptable for a control audience, but one sentence on strict versus nonstrict feasibility would help.

The stress-test note points at the real issue. The conditional theorem is true as stated; the missing piece is existence of the rank-one solution. I would not desk-reject this. A serious referee should ask for an existence or rank-reduction discussion and a reproducibility package, but the constructive result itself deserves to be in the literature.

Recommendation: send to peer review. I would cite it in work on dual instability certificates.

Referee Report

2 major / 5 minor

Summary. This paper addresses the absolute stability analysis of feedback systems with slope-restricted nonlinearities using IQC-based LMIs with static O'Shea-Zames-Falb multipliers. When the standard sufficient LMI for absolute stability is infeasible, the authors consider its dual. The main theorems (Theorem 1 for slope-restricted nonlinearities and Theorem 2 for slope-restricted and odd nonlinearities) state that if the dual LMI admits a rank-one feasible solution H = [h1; h2][h1; h2]^T, then a destabilizing nonlinearity within the assumed class can be explicitly constructed, and x(t) = h1 is a nonzero equilibrium of the resulting closed-loop system, implying the system is not absolutely stable. The paper provides constructive procedures for the destabilizing nonlinearity and illustrates the results with two numerical examples.

Significance. The paper proposes a novel and potentially valuable tool: a dual LMI certificate that not only detects non-absolute-stability but also provides a constructive destabilizing nonlinearity and an explicit equilibrium. The proofs of Theorems 1 and 2 are detailed and appear correct. The main limitation is that the results are conditional on the existence of a rank-one feasible dual solution, and the paper does not investigate when such a solution exists. If this rank-one condition can be shown to hold generically for infeasible primal LMIs, or if a reliable numerical procedure for finding rank-one solutions is provided, the contribution would be significant. In its current form, the paper is an interesting but incomplete answer to the problem it sets out to solve.

major comments (2)

[Section III.B (Theorem 1) and Section IV.B (Theorem 2)] The central hypothesis is the existence of a rank-one feasible solution H to the dual LMI (11)/(19). The paper does not show that primal infeasibility of (10)/(18) guarantees such a solution, nor does it provide a method to search for one. The two numerical examples only demonstrate rank-one solutions for particular systems. Since the dual feasible set is a convex cone, there is no general rank-reduction argument ensuring a rank-one element, and the theorems are vacuous for systems where all feasible dual solutions have rank greater than one. Please either provide a theoretical result on the existence of rank-one dual solutions, develop a numerical algorithm to find them, or explicitly state and discuss this limitation and adjust the claims in the abstract and introduction accordingly.
[Section III.D and Section IV.D] The numerical examples state that the dual LMI is feasible and that the solution H is 'numerically verified to be rank(H)=1,' but they do not explain how a rank-one solution was found or verified. Since the main theorems rely on the rank-one property, it is important to specify the optimization procedure (e.g., a rank-minimization heuristic such as nuclear norm minimization, or a tailored search). Without this, the examples are not reproducible and provide limited evidence that rank-one solutions can be found systematically.

minor comments (5)

[Section III.B, derivation of dual LMI (11)] The statement that the first inequality constraint in (9) has been replaced by an equality constraint in (11) is not explained; because the primal LMI (10) has P as a free symmetric variable, the dual should indeed contain He{AH11+BH12^T}=0, and this reasoning should be stated explicitly.
[Proof of Theorem 1, inequality (13)] The product in (13) is typeset ambiguously as `w∗_i − w∗_j / z∗_i − z∗_j (1 − ...)`; it should be written with parentheses around each quotient to make clear it is the product of two fractions.
[Proof of Theorem 1, part (ii)] The assertion that (13) and (14) 'clearly show the existence' of a slope-[0,1] function is terse; a short argument based on monotone piecewise linear interpolation with constant extension would make the proof self-contained.
[References] Reference [19] is a Japanese textbook; for the lemma He{uv^T}=0 with v≠0 implies u=0, consider giving a proof in the text or citing a standard linear algebra reference.
[Proof of Theorem 1, part (i)] There is a minor typo: 'to prove that rank(H)=1 can happen' should be 'can occur' or 'is possible'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the main theorems construct a destabilizing nonlinearity from a rank-one dual certificate; the missing rank-one existence proof is a completeness gap, not a circular reduction.

full rationale

The derivation chain is self-contained and does not reduce to its inputs. Proposition 1 and Lemma 1 come from Megretski-Rantzer and Fetzer-Scherer respectively, and are external published results, while the dual LMIs (9) and (17) are obtained by standard Lagrangian duality. Theorems 1 and 2 prove, rather than assume, that a rank-one dual solution yields an interpolating phi_wc in slope[0,1] via the nonnegativity arguments around Eqs. (12), (20), and (21), and a nonzero equilibrium x(t)=h1 via He{A h1 h1^T + B h2 h1^T}=0. The conclusion that the system is not absolutely stable is entailed by the rank-one hypothesis and the constructed phi_wc, not by a self-citation or by re-labelling a fitted parameter. The only notable weakness is that the paper does not show that primal infeasibility implies the existence of a rank-one dual solution; the numerical examples merely exhibit such a solution in two instances. That is a completeness and generality gap, not circularity. The self-citations to [17] and [19] are contextual or used for a standard linear algebra fact, and [20] is future work; none is load-bearing in the proof. Score 1 reflects the presence of minor self-citations while the central claim is derived independently and constructively.

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

No new physical entities or hidden fitting parameters. The paper's only constructive output is the piecewise-linear nonlinearity phi_wc, which is an allowed function in the assumed class, not an additional modeling assumption. The main unresolved assumption is the rank-one dual solution.

assumptions (5)

standard math Megretski-Rantzer IQC stability condition (Proposition 1): existence of P>0 and multiplier Pi in Pi_star satisfying LMI (4) implies stability.
Invoked in Lemma 2/Lemma 3 as the basis for the primal LMI; an external standard result.
domain assumption Fetzer-Scherer static OZF multiplier inequality (Lemma 1): for M doubly hyperdominant (doubly dominant for odd), the sector IQC holds for all slope-restricted nonlinearities.
External result [18] that defines the multiplier sets Pi^{m,DHD} and Pi^{m,DD}; not proved in this paper.
standard math Theorems of alternative for LMIs (Farkas lemma) as in [16].
Used to assert primal infeasibility iff dual LMI feasible; cited, not proved.
domain assumption Restriction to mu=0, nu=1 and ||D||<1 in Sections III.B and IV.B.
The extraction theorems are stated only for slope [0,1] and small direct feedthrough; the general-mu,nu dual is derived but not used for extraction.
ad hoc to paper Existence of a rank-one feasible solution H to the dual LMI (11)/(19).
This is the key hypothesis of Theorems 1 and 2; the paper does not establish when such a solution exists, only verifies it in two numerical examples.

how reviews work

0 comments

Cite this review

Pith. "Pith review of On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers." pith.science (2026). https://pith.science/paper/7WXBQBKK

@misc{pith2026241114339,
  author       = {Pith},
  title        = {Pith review of: On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WXBQBKK}},
  note         = {Machine review of arXiv:2411.14339}
}

read the original abstract

This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In existing works, well-known absolute stability certificates expressed in the IQC-based linear matrix inequalities (LMIs) were derived, in which the input-to-output characteristics of the slope-restricted nonlinearities were captured through static O'Shea-Zames-Falb multipliers. However, since these certificates are only sufficient conditions, they provide no clue about the absolute stability in the case where the LMIs are infeasible. In this paper, by taking advantage of the duality theory of LMIs, we derive a condition for systems to be not absolutely stable when the above-mentioned LMIs are infeasible. In particular, we can identify a destabilizing nonlinearity within the assumed class of slope-restricted nonlinearities as well as a non-zero equilibrium point of the resulting closed-loop system, by which the system is proved to be not absolutely stable. We demonstrate the soundness of our results by numerical examples.

Figures

Figures reproduced from arXiv: 2411.14339 by the authors.

**Figure 1.** Nonlinear Feedback System Σ B. Static O’Shea-Zames-Falb Multipliers Some specific definitions are necessary to describe static OZF multipliers. A matrix M ∈ R m×m is said to be Z-matrix if Mi,j ≤ 0 for all i ̸= j. Moreover, M is said to be doubly hyperdominant if it is a Z-matrix and M1m ≥ 0, 1 T mM ≥ 0, where 1m ∈ R m stands for the all-ones-vector. In addition, M is said to be doubly dominant if |M|d1m ≥ 0, 1 T m|… view at source ↗

**Figure 2.** The input-output map of the detected ϕwc [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** The state trajectories with initial conditions [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The input-output map of the detected ϕwc [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: The state trajectories with initial conditions [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Controller Design for Bilinear Neural Feedback Loops
eess.SY 2025-05 conditional novelty 6.0 of 10

The paper gives LMI-based controller synthesis guaranteeing local exponential stability for bilinear systems with neural networks in the loop.
Detecting Destabilizing Nonlinearities in Absolute Stability Analysis of Discrete-Time Feedback Systems
math.OC 2025-02 accept novelty 5.0 of 10

A rank-one dual-LMI solution yields a slope-restricted nonlinearity and a nonzero equilibrium that prove a discrete-time feedback system is not absolutely stable.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · cited by 2 Pith papers

[1]

Lessard, B

L. Lessard, B. Recht, and A. Packard, Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints. SIAM Journal on Optimization, vol. 26, no. 1, pp. 57–95, 2016

work page 2016
[2]

Revay, R

M. Revay, R. Wang, and I. R. Manchester, A Convex Parameterization of Robust Recurrent Neural Networks, IEEE Control Systems Letters, vol. 5, no. 4, pp. 1363–1368, 2021

work page 2021
[3]

Ebihara, H

Y . Ebihara, H. Waki, V . Magron, N. H. A. Mai, D. Peaucelle, and S. Tarbouriech, l2 Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks. The 2021 ECC Special Issue of the European Journal of Control, no. 62, pp. 99–104, 2021

work page 2021
[4]

Ebihara, H

Y . Ebihara, H. Waki, V . Magron, N. H. A. Mai, D. Peaucelle, and S. Tarbouriech, Stability Analysis of Recurrent Neural Networks by IQC with Copositive Multipliers. Proc. of the 60th Conference on Decision and Control, pp. 5098–5103, 2021

work page 2021
[5]

H. Yin, P. Seiler, and M. Arcak, Stability Analysis Using Quadratic Constraints for Systems with Neural Network Controllers, IEEE Transactions on Automatic Control, vol. 67, no. 4, pp. 1980–1987, 2022

work page 1980
[6]

C. W. Scherer, Dissipativity and Integral Quadratic Constraints: Tai- lored Computational Robustness Tests for Complex Interconnections, IEEE Control Systems Magazine, vol. 42, no. 3, pp. 115–139, 2022

work page 2022
[7]

de Souza, A

C. de Souza, A. Girard, and S. Tarbouriech, Event-Triggered Neural Network Control Using Quadratic Constraints for Perturbed Systems, Automatica, vol. 157, 2023

work page 2023
[8]

Tarbouriech, G

S. Tarbouriech, G. Garcia, G. Silva Jr., and I. Queinnec, Stability and Stabilization of Linear Systems with Saturating Actuators, Springer, 2011

work page 2011

Show all 20 references

[9]

Khalil, Nonlinear Systems

H. Khalil, Nonlinear Systems. Prentice Hall, 2002

2002
[10]

Valmorbida, R

G. Valmorbida, R. Drummond, and S. R. Duncan, Regional Analysis of Slope-Restricted Lurie systems, IEEE Transactions on Automatic Control, vol. 64, no. 3, pp. 1201–1208, 2018

2018
[11]

A. S. Fagundes, J.M. Gomes da Silva Jr., and S. Tarbouriech, A Hybrid Approach to the Stability Analysis of Sampled-Data Lur’e Systems, System & Control Letters, vol. 184, 2024

2024
[12]

O’Shea, An Improved Frequency Time Domain Stability Criterion for Autonomous Continuous Systems, IEEE Transactions on Auto- matic Control, vol

R. O’Shea, An Improved Frequency Time Domain Stability Criterion for Autonomous Continuous Systems, IEEE Transactions on Auto- matic Control, vol. 12, no. 6, pp. 725–731, 1967

1967
[13]

Zames and P

G. Zames and P. Falb, Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities, SIAM Journal on Control, vol. 6, no. 1, pp. 89—108, 1968

1968
[14]

Carrasco, M.C

J. Carrasco, M.C. Turner, and W.P. Heath, Zames-Falb Multipliers for Absolute Stability: From O’shea’s Contribution to Convex Searches. European Journal of Control, vol. 28, no. 1–19, 2016

2016
[15]

Megretski and A

A. Megretski and A. Rantzer, System Analysis via Integral Quadratic Constraints, IEEE Transactions on Automatic Control, vol. 42, no. 6, pp. 819–830, 1997

1997
[16]

C. W. Scherer, LMI Relaxations in Robust Control, European Journal of Control, vol 12, no. 1, pp. 3–29, 2006

2006
[17]

T. Yuno, S. Nishinaka, R. Saeki, Y . Ebihara, V . Magron, D. Peaucelle, S Zoboli, and S. Tarbouriech, Stability Analysis of Feedback Systems with ReLU Nonlinearities via Semialgebraic Set Representation, IFAC PapersOnline, vol. 58, no. 28, pp. 138–143, 2024

2024
[18]

Fetzer and C

M. Fetzer and C. W. Scherer, Absolute Stability Analysis of Discrete Time Feedback Interconnections, IFAC PapersOnline, vol. 50, no. 1, pp. 8447–8453, 2017

2017
[19]

Ebihara, System Control Using LMI, Morikita Syuppan Co., Ltd, Tokyo, 2012

Y . Ebihara, System Control Using LMI, Morikita Syuppan Co., Ltd, Tokyo, 2012. (in Japanese)

2012
[20]

T. Yuno, S. Nishinaka, R. Saeki, and Y . Ebihara, On Static O’Shea- Zames-Falb Multipliers for Idempotent Nonlinearities, Proc. Confer- ence on Decision and Control, 2024, to appear

2024

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Lessard, B

L. Lessard, B. Recht, and A. Packard, Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints. SIAM Journal on Optimization, vol. 26, no. 1, pp. 57–95, 2016

work page 2016

[2] [2]

Revay, R

M. Revay, R. Wang, and I. R. Manchester, A Convex Parameterization of Robust Recurrent Neural Networks, IEEE Control Systems Letters, vol. 5, no. 4, pp. 1363–1368, 2021

work page 2021

[3] [3]

Ebihara, H

Y . Ebihara, H. Waki, V . Magron, N. H. A. Mai, D. Peaucelle, and S. Tarbouriech, l2 Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks. The 2021 ECC Special Issue of the European Journal of Control, no. 62, pp. 99–104, 2021

work page 2021

[4] [4]

Ebihara, H

Y . Ebihara, H. Waki, V . Magron, N. H. A. Mai, D. Peaucelle, and S. Tarbouriech, Stability Analysis of Recurrent Neural Networks by IQC with Copositive Multipliers. Proc. of the 60th Conference on Decision and Control, pp. 5098–5103, 2021

work page 2021

[5] [5]

H. Yin, P. Seiler, and M. Arcak, Stability Analysis Using Quadratic Constraints for Systems with Neural Network Controllers, IEEE Transactions on Automatic Control, vol. 67, no. 4, pp. 1980–1987, 2022

work page 1980

[6] [6]

C. W. Scherer, Dissipativity and Integral Quadratic Constraints: Tai- lored Computational Robustness Tests for Complex Interconnections, IEEE Control Systems Magazine, vol. 42, no. 3, pp. 115–139, 2022

work page 2022

[7] [7]

de Souza, A

C. de Souza, A. Girard, and S. Tarbouriech, Event-Triggered Neural Network Control Using Quadratic Constraints for Perturbed Systems, Automatica, vol. 157, 2023

work page 2023

[8] [8]

Tarbouriech, G

S. Tarbouriech, G. Garcia, G. Silva Jr., and I. Queinnec, Stability and Stabilization of Linear Systems with Saturating Actuators, Springer, 2011

work page 2011