Robust Moving Horizon H∞ Control of Discrete Time‐Delayed Systems with Interval Time‐Varying Delays

Abstract

In this study, design of a delay‐dependent type moving horizon state‐feedback control (MHHC) is considered for a class of linear discrete‐time system subject to time‐varying state delays, norm‐bounded uncertainties, and disturbances with bounded energies. The closed‐loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time‐delay appeared in the system dynamics. Utilizing a discrete‐time Lyapunov‐Krasovskii functional, some delay‐dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run‐time, then we can construct a control law which guarantees the closed‐loop asymptotic stability, maximum disturbance rejection performance, and closed‐loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete‐time, time‐delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.