L2-L∞ filtering for stochastic systems driven by Poisson processes and Wiener processes

This paper investigates the L2-L∞ filtering problem for stochastic systems driven by Poisson processes and Wiener processes. Firstly, this paper presents an approach to transform the expectation of stochastic integral with respect to Poisson process into the expectation of Lebesgue integral by the martingale theory. Then, based on this, a filter is designed to guarantee that the filtering error system is mean-square asymptotically stable and its L2-L∞ performance satisfies a prescribed level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.