Proceedings ArticleDOI
Second-order counterexample to the discrete-time Kalman conjecture
Joaquin Carrasco,William P. Heath,Manuel De la Sen +2 more
- pp 981-985
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TLDR
The discrete-time Kalman conjecture is shown to be false for systems of order two and above, which contrasts with continuoustime domain systems where the KalMan conjecture is true for third-order systems.Abstract:
In this paper, the discrete-time Kalman conjecture is shown to be false for systems of order two and above. Counterexamples are constructed. This contrasts with continuoustime domain systems where the Kalman conjecture is true for third-order systems.read more
Citations
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Journal ArticleDOI
Second-order counterexamples to the discrete-time Kalman conjecture
TL;DR: A class of second-order discrete-time systems for which the Kalman conjecture is true provided the nonlinearity is odd, but false in general is discussed, which has strong implications for the analysis of saturated systems.
Journal ArticleDOI
Input-to-State Stability of Discrete-Time Lur'e Systems
Elvijs Sarkans,Hartmut Logemann +1 more
TL;DR: An input-to-state stability theory, which subsumes results of circle criterion type, is developed in the context of discrete-time Lur'e systems, inspired by the complexified Aizerman conjecture.
Posted Content
Duality bounds for discrete-time Zames-Falb multipliers
TL;DR: The numerical results allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex, and to discuss numerical examples where the limitations are stronger than others in the literature.
Proceedings ArticleDOI
Analysis of the Heavy-ball Algorithm using Integral Quadratic Constraints
Apurva Badithela,Peter Seiler +1 more
TL;DR: Results demonstrate that IQC condition is tight for the analysis of the tuned Heavy-ball, i.e. it yields the exact condition ratio that separates global convergence from non-global convergence for the algorithm.
Proceedings ArticleDOI
Stability analysis of asymmetric saturation via generalised Zames-Falb multipliers
TL;DR: Stability can be established using a sub-class of the Zames-Falb multipliers for asymmetric saturation in Lurye systems whose nonlinearity may be time-varying but is bounded above and below by time-invariant monotone nonlinearities.
References
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Book
Nonlinear Systems Analysis
TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.
Book
The stability of dynamical systems
TL;DR: In this paper, an introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method is presented and the main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations.
Journal ArticleDOI
Nonlinear Systems Analysis
TL;DR: Non-linear Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and proof of the Frobenius Theorem.
Journal ArticleDOI
System analysis via integral quadratic constraints
TL;DR: A stability theorem for systems described by IQCs is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality.
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Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach
TL;DR: The aim of this book is to provide a Discussion of the Foundations of Discrete-Time Optimal Nonlinear Feedback Control and its Applications in Dynamical Systems and Differential Equations, as well as some suggestions for further study.
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