Robust Moving HorizonH∞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.

Observer-based H2 controller design for a vibration isolation stage having hybrid electromagnets

“…In the last few decades, linear matrix inequalities (LMIs) have been intensively used as a strong tool in the field of control theory. Many problems, such as H 2 and H∞ state feedback and dynamic output feedback controller synthesis, 18 analysis and design of robustness against parametric uncertainties, 19,20 and stability of time delay systems 21,22 can all be reduced to convex or quasi-convex multiobjective problems that contain LMIs. 23 Due to successful improvements of efficient and reliable algorithms 24,25 for solving LMIs, such as interior point method, 26 these problems can now be solved in polynomial time.…”