Abstract
This paper addresses a robust H-infinity fuzzy filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with continuous random fluctuations, discontinuous Poisson jumping noise, random external disturbance and measurement noise in the spatio-temporal domain. For NSPDSs, the robust H-infinity filter design problem through a measurement output needs to solve a complex second-order Hamilton Jacobi integral inequality (HJII). In order to simplify the design procedure, a fuzzy stochastic partial differential system (FSPDS) based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, the robust H-infinity fuzzy filter design problem can be reformulated as a diffusion matrix inequality (DMI) problem. To solve a set of difficult DMIs for the H-infinity fuzzy filter via the traditional algebraic matrix techniques, we utilize the divergence theorem and Poincare inequality to transform the DMIs into bilinear matrix inequalities (BMIs), which could be easily transformed to a set of equivalent linear matrix inequalities (LMIs) by the proposed decoupling technique to simplify the design procedure of robust H-infinity fuzzy filter for NSPDSs. The proposed robust H-infinity fuzzy filter could efficiently attenuate the effect of spatio-temporal external disturbances on the filtering performance of NSPDSs. Finally, a robust state estimation problem of an ecology system with intrinsic spatio-temporal continuous Wiener noise and discontinuous Poisson jump fluctuations is provided to illustrate the design procedure and to confirm the H-infinity filtering performance of the proposed H-infinity fuzzy filter design method.