Observer-based controller synthesis for discrete systems under bounded peak disturbances: Convergence within ellipsoids

This paper investigates the problems of observer-based feedback controller synthesis for discrete-time linear systems under bounded peak disturbances. The control objective is to make the system state of the closed-loop system under bounded peak disturbances converges to an ellipsoid that is as small as possible or converges to a pre-specified ellipsoid. In order to determine the observer gain and feedback gain in the observer-based controller, the matrix decoupling technique is adopted to derive the single-step matrix inequality conditions. A numerical example is given to show the validity of the theoretical findings.