Robust H∞ filtering for nonlinear discrete-time singular Markov jump systems with time-varying delay

In this paper, H∞ filtering problem for a class of nonlinear uncertain discrete-time singular Markov jump systems with time-varying delay is discussed. The nonlinear function satisfies a quadratic constraint. First, a sufficient condition is given 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. With this condition, by using a series of matrix inequalities, another sufficient condition is obtained 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, by using linear matrix inequality (LMI), 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.