Fuzzy model-based robust H∞ filtering for a class of nonlinear nonhomogeneous Markov jump systems

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• T–S fuzzy model is employed to represent nonlinear nonhomogeneous Markov system.
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• Robust fuzzy filtering problem is studied for nonlinear nonhomogeneous Markov jump system.
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• Time varying transition probability matrix is described as a polytope set.
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• Filtering error system is stochastically stable and has a prescribed H∞H∞ performance index.

This paper studies the problem of robust fuzzy H∞H∞ filtering for a class of uncertain nonlinear discrete-time Markov jump systems with nonhomogeneous jump transition probabilities. The Takagi and Sugeno fuzzy model is employed to represent such nonlinear nonhomogeneous Markov jump system with norm-bounded parameter uncertainties. By Lyapunov function approach, under the designed mode-dependent and variation-dependent fuzzy filter which includes the membership functions, a sufficient condition is presented to ensure that the filtering error dynamic system is stochastically stable and has a prescribed H∞H∞ performance index. An example is given to demonstrate the effectiveness and advantages of the proposed techniques.