Robust Finite-Time H∞ Filtering for Discrete-Time Markov Jump Stochastic Systems

Aiqing Zhang
2018 Journal of Applied Mathematics and Physics  
This study is concerned with the problem of finite-time H ∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H ∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H ∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in
more » ... terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method. Journal of Applied Mathematics and Physics control problems for Markov Jump linear systems in [4]. In [5] [6] [7] [8] [9], some methods of H ∞ filtering design for Markov Jump systems or switched systems were proposed. As well known, Lyapunov asymptotic stability theory focuses on the steady-state behavior of plants over an infinite-time interval. But in many practical systems, it is only required that the system states remain within the given bounds. This motivated the introduction of finite-time stability or short-time stability, which has received considerable attention [10]-[19]. The authors investigated the sufficient conditions of finite-time stability for a class of stochastic nonlinear systems in [10]. The problem of robust finite-time stabilization for impulsive dynamical linear systems was investigated in [11]. In [12] fuzzy control method was adopted to solve finite-time stabilization of a class of stochastic system. A robust finite-time filter was established for singular discrete-time stochastic system in [13]. Some related works for finite-time problems were discussed in
doi:10.4236/jamp.2018.611201 fatcat:e7ba3h4r6fgwhjk62qybytvsta