Continuous-time state-feedback H-2-control of Markovian jump linear systems via convex analysis

Continuous-time H-2-control problem for the class of linear systems with Ma rkovian jumps (MJLS) using convex analysis is considered in this paper. The definition of the H-2-norm for continuous-time MJLS is presented and relat ed to the appropriate observability and controllability Gramians. A convex programming formulation for the H-2-control problem of MJLS is developed. T hat enables us to tackle the optimization problem of MJLS under the assumpt ion that the transition rate matrix Pi = [pi(ij)] for the Markov chain may not be exactly known, but belongs to an appropriate convex set. An equivale nce between the convex formulation when Pi is exactly known and the usual d ynamic programming approach of quadratic optimal control of MJLS is establi shed. It is shown that there exists a solution for the convex programming p roblem if and only if there exists the mean-square stabilizing solution for a set of coupled algebraic Riccati equations. These results are compared w ith other related works in the current literature. (C) 1999 Elsevier Scienc e Ltd. All rights reserved.