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

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. (c) 2019 Elsevier Inc. All rights reserved.