Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises

Abstract

This paper addresses the mean-square finite-dimensional filtering problem for polynomial system states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for system states described by polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order polynomial system. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.

Almost sure H∞ filtering for nonlinear hybrid stochastic systems with mode-dependent interval delays

“…[2,8,14,15,17,18,23,29,32,35] and the references therein. Commonly, the H ∞ filtering theory aims at designing a filter such that the H ∞ norm of the transfer function from the noise to the filtering error is not larger than a desired noise attenuation level [3,7,11]. Compared with the popular Kalman filtering approach, the H ∞ filtering method can be utilized to effectively improve the insensitivity against parameter uncertainties and external noises without the knowledge of their statistics.…”