Overlapping mode-dependent H<inf>∞</inf> control of discrete-time Markovian jump linear systems

This paper is concerned with overlapping mode-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a discrete-time Markov jump linear system in the presence of overlapping local operation modes and incomplete mode transition probabilities. By developing a randomly overlapping decomposition method, the system with deficient global operation modes is reformulated by a set of locally overlapping switched groups with accessible group and local modes. An overlapping group- and local-mode-dependent state feedback controller is delicately constructed. Unlike some existing controllers proposed in the literature, we do not require complete global mode information, but take full advantage of the knowledge of group and local modes of the reformulated system. Moreover, overlapping local modes are allowed to be existed in the formed groups. The stability analysis and control design procedures are developed based on the stochastic Lyapunov functional approach. The proposed framework is shown to be more general, which covers the traditional Markovian jump linear system with completely available global modes as a special case. In the case of only one local group, it is also shown that some existing results from the literature can be regarded as a special case of our derived results. A simulation example is finally presented to show the effectiveness and merits of the proposed method.