Robust H ∞ control of discrete‐time Markovian jump systems in the presence of incomplete knowledge of transition probabilities and saturating actuator

This paper deals with the problem of robust H _∞ control for a class of discrete‐time Markovian jump systems subject to both actuator saturation and incomplete knowledge of transition probability. Different from the previous results where the transition probability is completely known, a more general situation where only partial information on the exact values of elements in transition probability matrix is considered. By introducing some free parameters to express the relationship for the known and the unknown elements of transition probability matrix in stability analysis, a criterion is established to guarantee the stochastic stability of the closed‐loop system as well as an H _∞ performance index. The concept of domain of attraction in mean square sense is used to analyze the closed‐loop stability, and the mode‐dependent H _∞ state‐feedback controller is designed. It is shown that, even in the absence of actuator saturation, the obtained result is less conservative than the existing one. A numerical example is provided to illustrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.