Stability analysis of singular time-delay systems using the auxiliary function-based double integral inequalities. (English) Zbl 1483.93469
Summary: 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.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C43 | Delay control/observation systems |
Keywords:
singular time-delay systems; Lyapunov-Krasovskii functionals; delay-dependent matrix technique; auxiliary function-based integral inequalitiesReferences:
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