Composite slack-matrix-based integral inequality and its application to stability analysis of time-delay systems

This paper focuses on the delay-dependent stability problem of time-varying delay linear systems. A composite slack-matrix-based integral inequality (CSMBII) is presented in delay-product types. It overcomes the limitation of reciprocal convexity in Bessel-Legendre integral inequality such that CSMBII is more convenient to cope with time-varying delay systems. And it also overcomes the shortcoming that the slack matrices in previous works are independent of time-varying delay. Based on CSMBII, a new delay-dependent stability criterion is derived for time delay systems. A numerical example is given to illustrate the effectiveness of the stability criterion. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces a new composite slack-matrix-based integral inequality to address the stability problem of time-varying delay linear systems. This method overcomes some limitations in previous approaches and also presents a new stability criterion based on this inequality.