Dissipativity Analysis for Singular Time-Delay Systems Via State Decomposition Method.

This paper studies the dissipativity of singular time-delay systems. The objective is to derive a less conservative criterion with less computational demand. Throughout this paper, the augmented Lyapunov–Krasovskii functional (LKF) and the free-matrix-based integral inequality are used to realize less conservativeness. On the basis of these techniques, a less conservative criterion is first given. Then, by decomposing singular time-delay systems into differential equations and algebraic ones, state vectors of the systems are divided into two parts. To reduce redundant decision variables, each part of the state vectors is considered independently to construct a special augmented LKF with less decision variables. As a result, an improved criterion is deduced, and thus less conservativeness and less computational demand are achieved at the same time. Moreover, the presented state decomposition method provides a new research idea for singular time-delay systems not yet reported in the literatures. Finally, the above statements are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]