Robust ∞8 filtering for nonlinear discrete-time singular Markov jump systems

In this paper, H_∞ filtering problem for a class of nonlinear uncertain discrete-time singular Markov jump systems is discussed. The nonlinear function satisfies a quadratic constraint. First, a linear matrix inequality (LMI) sufficient condition is developed which guarantees that the nominal filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H_∞ performance. In order to facilitate the design of the filter, with this condition, by using a series of matrix inequalities, another LMI sufficient condition is obtained which guarantees that the nominal filtering error system is regular, causal, has unique solution in a neighborhood of the equilibrium point, is stochastically stable and satisfies H_∞ performance. Then, the design method of robust H_∞ filter in the form of standard Markov jump system is given, and the filter designed can be of full or of reduced order. Finally, a numerical example is given to verify the effectiveness and correctness of the proposed method.