In this paper, we first study the problems of robust quadratic mean square stability and stabilization for a class of uncertain discrete-time linear systems with both Markovian jumping parameters and Frobenius norm-bounded parametric uncertainties. Necessary and sufficient conditions for the above problems are proposed, which are in terms of positive definite solutions of a set of coupled algebraic Riccati inequalities. Then, the problem of robust quadratic guaranteed cost control for the underlying systems is investigated. A guaranteed cost control is designed to ensure the cost function is within a certain bound, irrespective of all admissible uncertainties. Furthermore, the control law and the bound are related to solutions of a set of coupled algebraic Riccati inequalities.
Published September 1997 , 25 pages