A further refinement of discretized Lyapunov functional method for the stability of time-delay systems

By Keqin Gu. 2001

260 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1632d3a43ca51bf8aec30fd44f5d17b9718b8db3

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In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay (2008, methodology): “When h1=0, the discretized Lyapunov functional method in [25] fails to conclude whether this system is stable or not.”
Hierarchy of LMI conditions for the stability analysis of time-delay systems (2015, methodology): “In this paper, we concentrate on this second method and introduce a set of new integral inequalities, which encloses the Jensen inequality [10] and the Improved Wirtinger-based inequality [27] as special cases.”
A Delay Decomposition Approach to Stability of Linear Neutral Systems (2008, background): “Time-delays are frequently encountered in many fields of science and engineering, including communication network, manufacturing systems, biology, economy and other areas (Hale and Verduyn Lunel, 1993; Gu et al., 2003). During the last two decades, the problem of stability of retarded and neutral ty”
Small gain problem in coupled differential‐difference equations, time‐varying delays, and direct Lyapunov method (2011, methodology): “Using Jensen inequality (Lemma 1 in [30]), it can be shown, considering zero initial condition and exchanging the order of integration, that”
Delay-dependent stability criteria for linear systems with multiple time delays (2006, unknown): “[1–22]).”
Delay-dependent stabilization of linear systems with time-varying state and input delays (2005, result): “On the other hand, when the symbol “ ” in (7) is replaced by “>”, it can easily be shown that the result obtained by using (6) and (7) to bound (18) is the same as that obtained by using (12) in combination with the variable elimination technique (Gu, 2001).”
A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays (2009, methodology): “In this paper, in order to obtain some less conservative sufficient conditions, inspired by the discretized Lyapunov functional method proposed by Gu [21], we decompose the delay interval [−h,0] into N equidistant subintervals, where N is a given integer, that is,”
A survey of linear matrix inequality techniques in stability analysis of delay systems (2008, methodology): “This theorem was generalised and used to deal with stability problems of different kinds of time-delay systems (see Gu 1999a,b,c; Gu 2001a,b; Gu, Han, Luo, and Niculescu 2001; Han and Gu 2001; Han 2002; Gu 2003a,b; Han, Gu, and Yu 2003; Han, Yu, and Gu 2004; Han 2005b).”
An improved stability criterion for systems with distributed delays (2001, methodology): “A result similar to condition II in Reference [10] is also possible, but will not be presented here due to space limitation.”