Finite-Time H ∞ Filtering for Singular Stochastic Systems

Abstract

This paper addresses the problem of finite-time $H_{\infty }$ 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 $H_{\infty }$ finite-time boundedness are presented. Then, the $H_{\infty }$ 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 $H_{\infty }$ 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.