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

ABSTRACT In this article, the observer‐based 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 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 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.