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

This paper deals with the problem of overlapping mode-dependent H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter design for discrete-time Markovian jump linear systems subject to randomly overlapping switching laws and incomplete transition probabilities. By employing a new overlapping decomposition method, the original Markovian jump linear system is reformulated by several local overlapping switched groups governed by some local overlapping Markov chains and a high-level homogeneous Markov chain. The proposed framework is shown to be more general, which covers the traditional widely studied Markovian jump linear systems as a special case. An overlapping local- and group-mode-dependent H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter is proposed. Based on the stochastic Lyapunov functional approach and the free weighting matrix technique, a new sufficient condition for the existence of such desired filter is established to ensure the stochastic stability and to guarantee a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> noise attenuation performance for the resulting filter error system. An illustrative example is given to show the effectiveness and feasibility of the proposed method.