Output feedback receding horizon stabilization and H∞ control for time-varying discrete-time systems

In this paper we consider the receding horizon stabilization and H-infinity control problems for time-varying discrete-time systems. We first consider the receding horizon stabilization control problem. We give design methods of receding horizon state feedback, output feedback controllers and observers. We then consider the receding horizon H-infinity control problems. We introduce two Riccati inequalities (equations) from the standard H-infinity theory, one for the state feedback controller and the other for the filter gain. We rewrite the second Riccati inequality and obtain an equivalent inequality for the inverse. We then rewrite this using LMI to obtain the final form of the inequality which is used to our receding horizon H-infinity control problem. We Live a numerical example and construct a receding horizon H-infinity controller.