Combined-slack-matrix-based integral inequality: Application to time-delay systems

Abstract

This paper proposes a new integral inequality, say combined-slack-matrix-based integral inequality, which extends a free-matrix-based integral inequality. For a single integral quadratic function, it provides a upper bound which depends on not only the concerned integration interval but also another integration interval. Consequently, the proposed integral inequality contains more flexibility, which contributes to developing an improved stability criterion for linear systems with interval-time varying delays.