H ∞ $$ {H}_{\infty } $$ PID Control for Singularly Perturbed Systems With Randomly Switching Nonlinearities Under Dynamic Event-Triggered Mechanism

In this article, the observer-based $H_{\infty }$ proportional-integral-derivative (PID) control problem is studied for a class of singular perturbed systems with randomly switching nonlinearities. During the modeling process, a set of binary random sequences is introduced to describe the random behaviors of the nonlinear switching encountered in engineering practice. Considering the singular perturbation parameter (SPP), an observer-based $H_{\infty }$ PID controller is constructed for the concerned singularly perturbed systems (SPSs), where the state information is estimated. To improve communication efficiency and reduce resource waste, a dynamic event-triggered mechanism is employed during the measurement transmission. Meanwhile, an SPP-dependent Lyapunov-Krasovskii function is utilized to derive conditions under which the closed-loop system is guaranteed to be stochastically stable with the desired $H_{\infty }$ performance under a specified upper bound on the SPP. All the desired observer and controller gains are determined by solving a set of matrix inequalities. Finally, the effectiveness and superiority of the suggested PID control method are verified through a simulation example.