Finite-time filtering for non-linear stochastic systems

Mingzhe Hou, Zongquan Deng and Guangren Duan

International Journal of Systems Science, 2016, vol. 47, issue 12, 2945-2953

Abstract: This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton–Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Date: 2016
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DOI: 10.1080/00207721.2015.1049302

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