Robust moving horizon hinf control of discrete time state-delayed systems

This thesis is concerned with design of a delay-dependent type moving horizon Hinf state-feedback control (MHHC) 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. The main objective is the development of possible low conservative stability condition for time delay systems and of a novel control method for such systems using dissipation constraint together with online adapting of the dissipation level. For that purpose, the constraint minimax optimization problem is dealt with in the framework of Linear Matrix Inequality (LMI), in which the maximization is realized over a set of uncertainties and bounded disturbances. Utilizing a discrete-time Lyapunov-Krasovskii (L-K) functional, some delay-dependent, LMI based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively in 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 and 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.