Resilient Dissipative Filtering for Uncertain Markov Jump Nonlinear Systems with Time-Varying Delays

The resilient dissipative filtering problem for a class of uncertain time-delay Markov jump nonlinear systems is studied in this paper. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system, and by constructing a new multiple Lyapunov–Krasovskii function, the sufficient conditions regarding the existence of desired resilient dissipative filters are obtained in terms of linear matrix inequalities, which ensure the filtering error system is stochastically stable and strictly dissipative. The designed filter can tolerate additive uncertainties in the filter gain matrix, which results from filter implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.