D-admissible hybrid control of a class of singular systems. (August 2015)

• Record Type: Journal Article
• Authors: Dong, Xin-zhuang; Xiao, Mingqing
• Is Part Of: Nonlinear analysis. Volume 17(2015)
• Page Start: 94
• Page End: 110
• Publication Date: 2015-08
• Subjects: Singular delta operator systems -- D-admissibility -- State feedback -- Lipschitz nonlinear perturbation -- Globally exponential stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2015.03.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.