Stability analysis of singular time-delay systems using the auxiliary function-based double integral inequalities

摘要

Recently, there have been a few developments reported on using the Wirtinger/free-matrix-based single integral inequality to stability problem of singular time-delay systems but there has been no report on the double ones. This paper presents an extension on applying the auxiliary function-based double integral inequality to the problem. Furthermore, an extension of the delay-dependent matrix technique into the single integral term of the Lyapunov-Krasovskii function to reduce more the conservatism has also been presented. By proposing an extended Lyapunov-Krasovskii functional (LKF) with triple integral terms and three delay-dependent matrices, a new delay-derivative-dependent stability criterion is derived. The effectiveness of the obtained result is illustrated through a numerical example.