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

••T–S fuzzy model is employed to represent nonlinear nonhomogeneous Markov system.••Robust fuzzy filtering problem is studied for nonlinear nonhomogeneous Markov jump system.••Time varying transition probability matrix is described as a polytope set.••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.