Sliding mode control with bounded ℒ2ℒ2 gain performance of Markovian jump singular time-delay systems

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 ℒ2ℒ2 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 ℒ2ℒ2 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 the 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.