Sliding mode control with bounded \(\mathcal L_2\) gain performance of Markovian jump singular time-delay systems. (English) Zbl 1268.93037

Wu, Ligang; Su, Xiaojie; Shi, Peng

Automatica 48, No. 8, 1929-1933 (2012).

Summary: In this paper, we investigate the problem of Sliding Mode Control (SMC) of Markovian jump singular time-delay systems. The aim is to consider the bounded \(\mathcal L_2\) gain performance in the analysis of sliding mode dynamics, thus to improve the transient performance of the SMC system. Firstly, a delay-dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded \(\mathcal L_2\) gain performance condition. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order singular Markovian jump time-delay system. Then, the sliding mode dynamics is analyzed and a solvability condition for the desired switching surface function is derived. Moreover, an SMC law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed techniques.

MSC:

93B12	Variable structure systems
60J75	Jump processes (MSC2010)

Keywords:

sliding mode control; singular systems; bounded \(\mathcal L_2\) gain performance; time-delay; Markovian jump singular time-delay systems; integral-type switching surface function; system trajectories; time-delayed system

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