Stability analysis of linear systems with time-varying delay via a quadratic function negative-definiteness determination method

摘要

This study aims to carry out the stability analysis of linear systems with a time-varying delay. It is known that the negative-definite condition of the derivative of a Lyapunov–Krasovskii functional (LKF) can be determined using the convex combination method if the convexity requirement is satisfied by the derivative of the LKF. However, this method is not feasible in cases where the LKF's derivative is a quadratic function. To address this problem, this study proposes a novel negative-definiteness determination lemma that encompasses the previous lemmas as its special cases and shows less conservatism. Then, this lemma is employed to derive a stability criterion, and its superiority is demonstrated using three examples.