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Robust filtering for a class of discrete‐time uncertain nonlinear systems: An H ∞ approach
Author(s) -
Xie Lihua,
De Souza Carlos E.,
Wang Youyi
Publication year - 1996
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/(sici)1099-1239(199605)6:4<297::aid-rnc234>3.0.co;2-v
Subject(s) - riccati equation , parametric statistics , nonlinear system , control theory (sociology) , discrete time and continuous time , mathematics , filtering problem , norm (philosophy) , filter (signal processing) , class (philosophy) , algebraic riccati equation , mathematical optimization , computer science , filter design , mathematical analysis , differential equation , control (management) , statistics , physics , quantum mechanics , artificial intelligence , political science , law , computer vision
Abstract This paper deals with the H ∞ filtering problem for a class of discrete‐time nonlinear systems with or without real time‐varying parameter uncertainty and unknown initial state. For the case when there is no parametric uncertainty in the system, we are concerned with designing a nonlinear H ∞ filter such that the induced l 2 norm of the mapping from the noise signal to the estimation error is within a specified bound. It is shown that this problem can be solved via one Riccati equation. We also consider the design of nonlinear filters which guarantee a prescribed H ∞ performance in the presence of parametric uncertainties. In this situation, a solution is obtained in terms of two Riccati equations.