RobustH₂control of Markovian jump systems with uncertain switching probabilities

This article deals with the robust H 2 control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H 2 performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H 2 performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.