Sliding Mode Control for Switching Singularly Perturbed Systems: Adopting Nonhomogeneous Sojourn Probabilities

This paper is devoted to the sliding mode control issue of switching singularly perturbed systems in the presence of dynamic-memory event-triggered protocol. A novel nonhomogeneous sojourn probability is introduced with the hope of better characterizing the switching behavior of the corresponding system mode, in which the variation of sojourn probabilities is adjusted by a deterministic switching signal. Additionally, aiming at relieving the communication burden and improving improve the system performance, a novel dynamic event-triggered protocol with the merits of utilizing a series of historically launched packets and the singularly perturbed parameter is constructed. Subsequently, a singularly-perturbed-parameter-based sliding mode controller is designed for ensuring the mean-square exponential stability of the switching singularly perturbed systems and the reachability of the specified sliding surface. Finally, two simulation examples are provided to verify the efficiency of the theoretical findings. Note to Practitioners-Sliding mode control has gained broad attention for its cost-saving and reliability. In some practical networked control systems, due to the inner property, they will bring a great burden of computation and data transmission. In this paper, we give a novel dynamic event-triggered protocol with the merits of utilizing a series of historically launched packets and the singularly perturbed parameter. A novel nonhomogeneous sojourn probability is introduced with the hope of better characterizing the switching behavior of the corresponding system mode, in which the variation of sojourn probabilities is adjusted by a deterministic switching signal. A singularly-perturbed-parameter-based sliding mode controller is provided to make the networked control systems keep stable. The results provide a reference for the mean-square exponential stability of the switching singularly perturbed systems and the reachability of the specified sliding surface under sliding mode control.

Automated summary

This paper focuses on the sliding mode control of switching singularly perturbed systems in the presence of dynamic-memory event-triggered protocol. By introducing a novel nonhomogeneous sojourn probability and a dynamic event-triggered protocol, a singularly-perturbed-parameter-based sliding mode controller is designed and its efficiency is verified through simulation examples.