A CONVEX-PROGRAMMING APPROACH TO H-2 CONTROL OF DISCRETE-TIME MARKOVIAN JUMP LINEAR-SYSTEMS

In this paper we consider the H-2-control problem for the class of dis crete-time linear systems with parameters subject to markovian jumps u sing a convex programming approach. We generalize the definition of th e H-2 norm from the deterministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians. Conditions for existence and derivation of a mean square st abilizing controller for a markovian jump linear system using convex a nalysis are established. The main contribution of the paper is to prov ide a convex programming formulation to the H-2-control problem, so th at several important cases, to our knowledge not analysed in previous work, can be addressed. Regarding the transition matrix P = [p(ij)] fo r the Markov chain, two situations are considered: the case in which i t is exactly known, and the case in which it is not exactly known but belongs to an appropriated convex set. Regarding the state variable an d the jump variable, the cases in which they may or may not be availab le to the controller are considered. If they are not available, the H- 2-control problem can be written as an optimization problem over the i ntersection of a convex set and a set defined by nonlinear real-valued functions. These nonlinear constraints exhibit important geometrical properties, leading to cutting-plane-like algorithms. The theory is il lustrated by numerical simulations.