Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality

Abstract

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.