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Nonlinear H ∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay
Author(s) -
Yang Yuxia,
Lin Chong,
Chen Bing
Publication year - 2018
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.4391
Subject(s) - lipschitz continuity , control theory (sociology) , nonlinear system , mathematics , observer (physics) , discrete time and continuous time , linear matrix inequality , quadratic growth , bounded function , exponential stability , stability (learning theory) , mathematical analysis , computer science , mathematical optimization , control (management) , statistics , physics , quantum mechanics , artificial intelligence , machine learning
Summary This paper investigates the H ∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H ∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ . The synthesis condition of H ∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.