Event-Triggered \(H_{\infty }\) Sliding Mode Control for Discrete-Time Singular Markov Jump Systems with Uncertainties in the Difference Matrix

This paper investigates the sliding mode control (SMC) problem of discrete-time singular Markovian jump systems with time-varying delay under an event-triggered strategy (ETS). In the system we study, there are uncertainties in the system matrix, especially in the difference matrix. A state augmentation strategy is proposed due to uncertainties in the difference matrix. A suitable sliding mode surface (SMS) function is built, and the corresponding sliding mode dynamics (SMD) is derived based on ETS. Some sufficient conditions are presented to guarantee that SMD is \(H_{\infty }\) $H_{\infty }$ -admissible for all uncertainties. Furthermore, an SMC law under ETS is derived so that the system trajectories can be driven onto the prescribed SMS in finite time. Finally, the effectiveness of the approach in the paper is demonstrated by two simulated examples.