A robust ℋ∞ observer‐based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities. (20th July 2015)

• Record Type: Journal Article
• Authors: Kheloufi, H.; Zemouche, A.; Bedouhene, F.; Souley‐Ali, H.
• Is Part Of: International journal of robust and nonlinear control. Volume 26:Number 9(2016)
• Page Start: 1962
• Page End: 1979
• Publication Date: 2015-07-20
• Subjects: Lipschitz condition -- nonlinear systems -- observer‐based stabilization -- ℋ∞ synthesis -- linear matrix inequalities (LMIs) -- linear parameter varying (LPV) approach; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3391
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper deals with the robust observer‐based ℋ ∞ control design for a class of Lipschitz nonlinear discrete‐time systems with parameter uncertainties. Based on the use of a reformulated Lipschitz property combined with the slack variable techniques and some mathematical artifacts, it is shown that the solution of the discrete‐time output feedback stabilization problem is conditioned by a set of bilinear matrix inequalities, which become linear matrix inequalities by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples are provided to show the validity and superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.