H∞ control for discrete‐time Markovian jump linear systems with partially uncertain transition probabilities

Abstract

SummaryThis work is concerned with the H∞ state‐feedback control for the discrete‐time Markovian jump systems with incomplete knowledge of transition probabilities. A less conservative criterion is proposed via linear matrix inequalities (LMIs) such that the considered systems are stochastically stable and have a prescribed H∞ disturbance attention level. Furthermore, based on the obtained results, a state‐feedback controller is presented via LMIs to guarantee the stochastic stability of the resulted closed‐loop system with a prescribed H∞ performance level γ. The number of the LMIs to be solved in the developed methods is much less than that in many existing methods. A numerical example and a practical example are provided to verify the effectiveness of the presented methods.