ℋ∞ control of discrete‐time Markov jump systems with bounded transition probabilities

This paper deals with the class of discrete‐time linear systems with random abrupt changes and unknown transition probabilities but varying between known bounds for each mode. The ℋ︁ ∞ control problem of this class of systems is revisited and new sufficient conditions are developed in the linear matrix inequality (LMI) setting to design the state‐feedback controller that stochastically stabilizes the system under consideration and at the same time guarantees the disturbance rejection with a desired level γ . Sufficient conditions for existence of the state‐feedback controller are developed. It is shown that the addressed problem can be solved if the corresponding developed LMIs are feasible. Numerical examples are employed to show the usefulness of the proposed results.