H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems

This paper concerns the problem of H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H∞ performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the H∞ filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results.