Abstract
Since the nonlinear dynamic systems in engineering, economics and biology may suffer from both continuous Wiener process and discontinuous Poisson process, the robust filter design for a class of nonlinear stochastic Poisson jump systems with external disturbances is studied in this paper. At present, there exists no good filter design method to treat the discontinuous Poisson process filter problem. Based on Ito-Levy formula, a robust H ∞ filter design is proposed for nonlinear stochastic Poisson jump systems by solving a Hamilton-Jacobi inequality (HJI) for the robust filter design of nonlinear stochastic Poisson jump system. The optimal H ∞ robust filter design problem for the nonlinear stochastic Poisson jump system is also discussed in this study.