Journal ArticleDOI
Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
TLDR
For a class of differential inclusions, to which many of the practically important control systems can be reduced, necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of Lyapunov functions.About:
This article is published in Systems & Control Letters.The article was published on 1989-06-01. It has received 433 citations till now. The article focuses on the topics: Differential inclusion & Lyapunov function.read more
Citations
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Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Journal ArticleDOI
Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
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Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
Hai Lin,Panos J. Antsaklis +1 more
TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
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Perspectives and results on the stability and stabilizability of hybrid systems
TL;DR: In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.
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Stability Criteria for Switched and Hybrid Systems
TL;DR: This paper considers the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws, and discusses the theory of Lyapunov functions and the existence of converse theorems.
References
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Journal ArticleDOI
Control of large-scale dynamic systems by aggregation
TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.
Journal ArticleDOI
Asymptotic behavior for differential equations which cannot be locally linearized
Andrzej Lasota,Aaron Strauss +1 more
TL;DR: In this paper, the authors define a multi-valued differential Df and prove that if all solutions of the multivalued differential equation u′ ϵ Df(u) approach zero as t → ∞, then all solutions x(·) of x′ = ƒ(x) with small |x(0)| approach zero exponentially as t→ ∞.
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On matrix measures and convex Liapunov functions
TL;DR: It is shown that this “modified” matrix measure has most of the properties of the usual matrix measure, and that many of the known applications of theusual matrix measure can be carried over to the modified matrix measure.