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Note on stability of linear systems with time-varying delay. (English) Zbl 1227.93089

Summary: This note considers the stability of linear systems with a time-varying delay. We are interested in a simple Lyapunov-Krasovskii Functional (LKF) approach without delay decomposition. In this category, all recent tractable results have a fixed bound on the allowable maximum size of the delay for years. We propose a new simple LKF including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function, and present a new result expressed in the form of LMIs. We show, by two well-known examples, that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time-delay.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05 Linear systems in control theory
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