A generalized multiple integral inequality with application to time-varying delay systems

This paper aims to investigate a generalized multiple integral inequality that is applied to drop the conservativeness of the stability criterion for time-varying delayed system. First, a more general multiple integral inequality is introduced by utilizing Schmidt-orthogonal method with integral operation and inequality techniques. Then, the inequality obtained is adopted to study the time-delay system, which yields the delay-related stability criterion with fewer conservatism. Finally, numerical examples are given to certify that the acquired inequality plays a crucial role in stability analysis.