## New conditions for delay-derivative-dependent stability.(English)Zbl 1180.93080

Summary: Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of P. Park and J. W. Ko [Automatica 43, No. 10, 1855–1858 (2007; Zbl 1120.93043)]. In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov-Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C05 Linear systems in control theory

### Keywords:

time-varying delay; Lyapunov-Krasovskii functional; LMI

Zbl 1120.93043
Full Text:

### References:

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