## New insight into delay-dependent stability of time-delay systems.(English)Zbl 1312.93077

Summary: This paper presents a new insight into the delay-dependent stability for time-delay systems. Because of the key observation that the positive definiteness of a chosen Lyapunov-Krasovskii functional does not necessarily require all the involved symmetric matrices in the Lyapunov-Krasovskii functional to be positive definite, an improved delay-dependent asymptotic stability condition is presented in terms of a set of LMIs. This fact has been overlooked in the development of previous stability results. The importance of the present method is that a vast number of existing delay-dependent results on analysis and synthesis of time-delay systems derived by the Lyapunov-Krasovskii stability theorem can be improved by using this observation without introducing additional variables. The reduction of conservatism of the proposed result is both theoretically and numerically demonstrated. It is believed that the proposed method provides a new direction to improve delay-dependent results on time-delay systems.

### 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
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