Proceedings ArticleDOI
An integral inequality in the stability problem of time-delay systems
Keqin Gu
- Vol. 3, pp 2805-2810
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In this paper, an integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation, and a simpler stability criterion is derived.Abstract:
An integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation. As the result, a simpler stability criterion is derived.read more
Citations
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Book
Stability of Time-Delay Systems
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
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Global exponential stability of generalized recurrent neural networks with discrete and distributed delays
TL;DR: A linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable, and the existence and uniqueness of the equilibrium point under mild conditions is proved.
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Technical communique: Improved delay-range-dependent stability criteria for linear systems with time-varying delays
TL;DR: A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms and some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices.
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Technical communique: Absolute stability of time-delay systems with sector-bounded nonlinearity
TL;DR: Some new delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) and improve the estimate of the stability limit over some existing result.
Journal ArticleDOI
Delay-dependent stabilization of linear systems with time-varying state and input delays
TL;DR: A new integral inequality for quadratic terms is first established and used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller.
References
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Book
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
Introduction to Functional Differential Equations
TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
Book
Interior-Point Polynomial Algorithms in Convex Programming
TL;DR: This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.