A generalized multiple-integral inequality and its application on stability analysis for time-varying delay systems

摘要

This paper is concerned with the stability analysis of time-delay systems. Lyapunov-Krasovskii functional method is utilized to obtain stability criteria in the form of linear matrix inequalities. The main purpose is to obtain less conservative stability criteria by reducing the estimation gap of the time derivative of the constructed Lyapunov-Krasovskii functional. First, a generalized multiple-integral inequality is put forward based on Schur complement lemma. Then, some special cases of the proposed generalized multiple-integral inequality are given to estimate single and double integral terms in the derivative of Lyapunov-Krasovskii functional. Furthermore, less conservative stability criteria are derived. Finally, three examples are given to illustrate the improvement of the proposed criteria. (C) 2019 Published by Elsevier Ltd on behalf of The Franklin Institute.