Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional

Abstract

This paper is concerned with the stability analysis of continuous linear systems with two additive time-varying delays in the Lyapunov–Krasovskii functional (LKF) framework. Two novel delay-product-type terms are introduced into LKF candidate inspired by our previous research. The Wirtinger-based inequality, together with the reciprocally convex combination technique, is applied to estimate the integral terms arising in the derivative of the LKF. As a result, a new delay- and its-change-rate-dependent stability criterion is established. Its advantage of less conservatism than some existing criteria is demonstrated through a numerical example. Finally, the stability criterion is applied to analyze the stability of the load frequency control scheme of power systems.