Event-based sliding mode control for singularly perturbed systems with switching parameters

This paper addresses the event-based sliding mode control problem for singularly perturbed systems with switching parameters. Unlike traditional Markovian switching systems, singularly perturbed S-MSSs allow more flexible state transitions, which can be described by a general distribution rather than the exponential distribution assumed in Markovian switching systems. To enhance the performance of such systems, a novel memory-based dynamic event-triggered protocol (DETP) is proposed, incorporating a memory term for the auxiliary offset variable. This approach reduces the frequency of communication packets, leading to more efficient transmission scheduling. The proposed memory-based DETP distinguishes itself by utilizing both the memory term and the singular perturbation parameter, effectively mitigating communication overhead while maintaining control performance. In addition, an innovative integral-type sliding surface is constructed, and a hidden semi-Markovian switching model is employed to address mode mismatches between the original system and the sliding mode control law. Using parameter-dependent Lyapunov theory, several sufficient conditions are derived to guarantee the exponential mode stability under bounded disturbances (EMSUB) behavior of the sliding mode dynamics. Finally, the effectiveness of the proposed control strategy is demonstrated through two simulation examples.