Reduced order dynamic output feedback control of uncertain discrete-time markov jump linear systems.

Abstract

This paper deals with the problem of designing reduced order robust dynamic output feedback controllers for discretetime Markov jump linear systems (MJLS) with polytopic state space matrices and uncertain transition probabilities. Starting from a full order, mode-dependent and polynomially parameter-dependent dynamic output feedback controller, sufficient linear matrix inequality based conditions are provided for the existence of a robust reduced order dynamic output feedback stabilizing controller assuring an upper bound to the H∞ or the H2 norm of the closedloop system. The main advantage of the proposed method when compared to the existing approaches is the fact that the the decision variables of the problem. In other words, the matrices that define the controller realization do not depend explicitly on the state space matrices associated to the modes of the MJLS. As a consequence, the method is specially suitable to handle order reduction or cluster availability constraints in the context ofH∞ orH2 dynamic output feedback control of discrete-time MJLS. Additionally, as illustrated by means of numerical examples, the proposed approach can provide less conservative results than other conditions in the literature.