Robust filtering with stochastic nonlinearities and multiple missing measurements. (English) Zbl 1168.93407

Wei, Guoliang; Wang, Zidong; Shu, Huisheng

Automatica 45, No. 3, 836-841 (2009).

Summary: This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval \([0,1]\). Such a probabilistic distribution could be any commonly used discrete distribution over the interval \([0,1]\). The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the Linear Matrix Inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.

MSC:

93E11	Filtering in stochastic control theory
93C10	Nonlinear systems in control theory
93C41	Control/observation systems with incomplete information

Keywords:

stochastic systems; nonlinear systems; uncertain systems; time-delay; missing measurements

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