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State‐saturated H ∞ filtering with randomly occurring nonlinearities and packet dropouts: the finite‐horizon case
Author(s) -
Ding Derui,
Wang Zidong,
Shen Bo,
Shu Huisheng
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2850
Subject(s) - filtering problem , bernoulli distribution , control theory (sociology) , mathematics , bernoulli's principle , bounded function , nonlinear system , network packet , filter (signal processing) , state (computer science) , norm (philosophy) , h infinity methods in control theory , convex hull , attenuation , filter design , regular polygon , random variable , computer science , algorithm , mathematical analysis , control (management) , statistics , engineering , physics , optics , artificial intelligence , geometry , quantum mechanics , political science , computer vision , law , aerospace engineering , computer network
SUMMARY This paper deals with the H ∞ filtering problem for a class of discrete time‐varying systems with state saturations, randomly occurring nonlinearities as well as successive packet dropouts. Two mutually independent sequences of random variables that obey the Bernoulli distribution are employed to describe the random occurrence of the nonlinearities and packet dropouts. The purpose of the addressed problem is to design a time‐varying filter such that the H ∞ disturbance attenuation level is guaranteed, over a given finite‐horizon, for the filtering error dynamics in the presence of saturated states, randomly occurring nonlinearities, and successive packet dropouts. By introducing a free matrix with its infinity norm less than or equal to 1, the error state is bounded by a convex hull so that some sufficient conditions obtained via solving a certain set of recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when state saturations are partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed filter design approach. Copyright © 2012 John Wiley & Sons, Ltd.