Stability and stabilization for discrete-time Markovian jump quadratic systems with incomplete knowledge of transition probabilities

This work firstly deals with the problems of stability and stabilization for discrete-time Markovian jump quadratic systems with incomplete knowledge of transition probabilities. By using the concept of domain of attraction in mean square sense, a method is derived to guarantee the stochastic stability, while providing an enlarged stability domain for the unforced system. The stability method is then extended to the stabilization problem and a sufficient condition for determining a nonlinear state feedback controller and an admissible initial domain such that the resulting closed-loop system is stochastically stable for every initial condition from the admissible initial set is presented. Both the developed control methods are casted in terms of feasibility problems involving linear matrix inequalities (LMIs). Two simulation examples are presented to show the effectiveness of the proposed technique.