On matrix measures and convex Liapunov functions
TLDR
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.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1978-01-01 and is currently open access. It has received 35 citations till now. The article focuses on the topics: Symmetric matrix & Matrix 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.
Book
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
Journal ArticleDOI
Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
TL;DR: 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.
Journal ArticleDOI
Constructive stability and asymptotic stability of dynamical systems
Robert K. Brayton,C. Tong +1 more
TL;DR: In this article, the authors presented an algorithm for constructing a Liapunov function for a dynamical system, and showed that the algorithm can be used in proving the asymptotic stability of dynamical systems, both difference and differential equations.
Journal ArticleDOI
Vector norms as Lyapunov functions for linear systems
TL;DR: A unified theory of quadratic and piecewise-linear Lyapunov functions for continuous and discrete-time linear systems is presented and sufficient and necessary conditions for a vector norm to be a Lyap unov function are presented.
References
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Feedback Systems: Input-output Properties
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.