Sliding-Mode Control for Slow-Sampling Singularly Perturbed Systems Subject to Markov Jump Parameters

This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters. As a new attempt, the SMC strategy is considered in the study of discrete-time Markov jump SPSs. Subsequently, in order to design a sliding-mode controller to ensure the stability of the proposed system, a novel integral sliding surface is constructed, and an SMC law is synthesized to ensure the reachability of the sliding surface. Through the utilization of Lyapunov stability and SMC theory, sufficient conditions are derived to ensure the state trajectories of the system are driven to a predefined sliding surface and the closed-loop sliding mode dynamics are stochastically stable. Finally, the applicability of the proposed SMC strategy is verified by a numerical example and a practical electric circuit model.

Automated summary

This article investigates the application of sliding-mode control in slow-sampling singularly perturbed systems with Markov jump parameters, ensuring system stability by constructing a novel integral sliding surface and synthesizing an SMC law. The study derives conditions to ensure state trajectories are driven to a predefined sliding surface and closed-loop sliding mode dynamics are stochastically stable, with the effectiveness of the proposed SMC strategy validated through numerical examples and a practical electric circuit model.