Finite‐Time H∞ Filtering for Singular Stochastic Systems

Caixia Liu,Yingqi Zhang,Huixia Sun

doi:10.1155/2012/615790

Abstract

This paper addresses the problem of finite‐time H∞ filtering for one family of singular stochastic systems with parametric uncertainties and time‐varying norm‐bounded disturbance. Initially, the definitions of singular stochastic finite‐time boundedness and singular stochastic H∞ finite‐time boundedness are presented. Then, the H∞ filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite‐time boundedness of the filtering error system and satisfy a prescribed H∞ performance level in some given finite‐time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.

Highlights

Singular systems referred to as descriptor systems or generalized state-space systems represent one family of dynamical systems since it generalizes the linear system model and has extensive applications in economics systems, power systems, mechanics systems, chemical processes, and so on; see for more practical examples 1, 2 and the references therein
We deal with the problem of finite-time H∞ filtering for a class of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance
Designed algorithms are provided to guarantee the filtering error system SSFTB and satisfy a prescribed H∞ performance level in a given finite-time interval, which can be reduced to feasibility problems involving restricted linear matrix equalities with a fixed parameter

Summary

Introduction

Singular systems referred to as descriptor systems or generalized state-space systems represent one family of dynamical systems since it generalizes the linear system model and has extensive applications in economics systems, power systems, mechanics systems, chemical processes, and so on; see for more practical examples 1, 2 and the references therein. Many control results in state-space systems have been extended to singular systems, such as stability, stabilization, H∞ control, and the filtering problems, for instance, see 3– 6 and the references therein. Markovian jump systems are referred to as one special family of hybrid systems and stochastic systems, which are very appropriate to model plants whose structure is subject to random abrupt changes, see the reference 7. Many attracting results have been studied, such as stochastic stability and stabilization 8, 9 , robust control 10–12 , guaranteed cost control 13 , and other issues. The problem of state estimation for singular Markovian jump systems has attracted considerable attention. As far as we know, the traditional Kalman filtering requires the exact knowledge of statistics of the noise

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Conclusion