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Zbl 1185.93111
Zhang, Wei; Cai, Xiu-Shan; Han, Zheng-Zhi
Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations. (English)
[J] J. Comput. Appl. Math. 234, No. 1, 174-180 (2010). ISSN 0377-0427

Summary: This paper considers the robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. A Lyapunov-Krasovskii functional, which takes the range information of the time-varying delay into account, is proposed to analyze the stability. A new approach is introduced for estimating the upper bound on the time derivative of the Lyapunov-Krasovskii functional. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criteria are established in terms of linear matrix inequalities. Numerical examples are given to show the effectiveness of the proposed approach.

MSC 2000:: *93D09 Robust stability of control systems
93C73 Perturbations in control systems
93C10 Nonlinear control systems

Keywords: Lyapunov-Krasovskii functional; delay-dependent stability; time-varying delay; nonlinear perturbations; linear matrix inequality (LMI)

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