Abstract
This paper addresses the problem of finite-time H∞ filter design for a class of non-linear stochastic systems with Markovian switching. Based on stochastic differential equations theory, a mode-dependent finite-time H∞ filter is designed to ensure finite-time stochastic stablility (FTSS) of filtering error system and satisfies a prescribed H∞ performance level in some given finite-time intervals. Moreover, sufficient conditions are presented for the existence of a finite-time H∞ filter for the stochastic system under consideration by employing the linear matrix inequality technique. Finally, the explicit expression of the desired filter parameters is given.
Highlights
Since filtering plays an important role in control systems, signal processing and communication, there has been a rapidly growing interest in filter designing due to its advantages over the traditional Kalman filtering
This paper addresses the problem of finite-time H∞ filter design for a class of non-linear stochastic systems with Markovian switching
Sufficient conditions are presented for the existence of a finite-time H∞ filter for the stochastic system under consideration by employing the linear matrix inequality technique
Summary
Since filtering plays an important role in control systems, signal processing and communication, there has been a rapidly growing interest in filter designing due to its advantages over the traditional Kalman filtering. H∞ filtering problems for discrete-time nonlinear stochastic systems were addressed in [2]. The problem of finite-time stability and stabilization for a class of linear systems with time delay was addressed in [15]. Finite-time H∞ filtering was proposed respectively for T-S fuzzy systems, switched systems, nonlinear singular systems, Itô stochastic Markovian jump systems in [20] [21] [22] [23]. Motivated by the contributions mentioned above, we investigated the mode-dependent finite-time filtering problems for stochastic nonlinear systems, which could be used to detect generation of residuals for fault diagnosis problems. The symbol * in a matrix denotes a term that is defined by symmetry of the matrix
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