Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality

摘要

This paper focuses on stability analysis of linear systems with time-varying delay, where two cases of the time-varying delay are discussed, that is, the time-varying delay is either differentiable or just uniformly continuous. First, an improved triple-integral inequality is proposed to estimate triple-integrals tightly. Then, by introducing two novel Lyapunov-Krasovskii functionals catering for two cases of time-varying delay, two sufficient conditions on stability, respectively, for the system under two cases of time-varying delay are derived using the improved triple-integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently. Finally, three numerical examples show that the obtained results outperform some existing ones. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.