Protocol-based SMC for singularly perturbed switching systems with sojourn probabilities

Abstract

This paper focuses on the finite-time sliding mode control for singularly perturbed switching systems in the presence of sojourn probabilities. To effectively capture the dynamic behavior of singularly perturbed switching systems, a generalized framework of piecewise-homogeneous sojourn probabilities is established. Additionally, a novel event-triggered protocol is introduced to alleviate transmission frequency, making use of dynamic quantization and adjustable triggering thresholds to accommodate system state fluctuations. Besides, an asynchronous sliding mode control law is designed, using a suitable sliding function and hidden-Markov model strategy, to ensure the trajectory of the resulting singularly perturbed switching systems reaches the predefined sliding surface within a finite-time interval. Finally, the proposed method is validated using a numerical example and two practical models, demonstrating its effectiveness and practicality.