New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Abstract

This paper focuses on the stability problems of continuous linear systems with two additive time-varying delay components. Firstly, an effective and simple Lyapunov–Krasovskii functional (LKF) is established, which not only takes adequate information of delay components and their upper bounds into consideration but also establishes a simpler form to decrease the computational complexity. Secondly, an improved delay-dependent stability criterion together with its corollary is obtained by employing the generalized free-weighting-matrix-based (GFWM-based) inequality and some other techniques to calculate the derivative of the constructed LKF, which will further reduce the introduced estimation error and make the criteria less conservative. Lastly, a numerical example is presented to illustrate the less conservatism and lower computational complexity of the derived results.