H_∞ State Estimation for Linear Continuous-Time Systems Driven by Wiener and Poisson Processes

Abstract

While H_∞ filtering theory for stochastic continuous-time systems driven by Poisson processes has been presented by B. Song et al.([21]), H_∞ smoothing theory for the systems and the relationship between H_∞ filtering and smoothing have not been yet fully investigated. In this paper, we study the H∞ state estimation (filtering and smoothing) problems for a class of linear continuous-time systems driven by Wiener and Poisson processes on the finite time interval. In order to derive H_∞ state estimators, we adopt unified stochastic variational approach as [15, 17] which has not been found in previous work by any other researchers.