Constrained quadratic state feedback control of discrete-time Markovian jump linear systems

In this paper we consider the quadratic optimal control problem of a discre te-time Markovian jump linear system, subject to constraints on the state a nd control variables. It is desired to find a state feedback controller, wh ich may also depend on the jump variable, that minimizes a quadratic cost a nd satisfies some upper bounds on the norms of some random variables, relat ed to the state and control variables of the system. The transition probabi lity of the Markov chain and initial condition of the system may belong to appropriate convex sets. We obtain an approximation for the optimal solutio n of this problem in terms of linear matrices inequalities, so that convex programming can be used for numerical calculations. Examples are presented to illustrate the usefulness of the developed results. (C) 1999 Elsevier Sc ience Ltd. All rights reserved.