D-admissible hybrid control of a class of singular systems |
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| Affiliation: | 1. College of Automation Engineering, Qingdao University, Qingdao 266071, China;2. Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA;1. School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran;2. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway;1. Laboratory for Ground Stone Tools Research, Zinman Institute of Archaeology, University of Haifa, Mount Carmel, Haifa 3498838, Israel;2. Zinman Institute of Archaeology, University of Haifa, Mount Carmel, Haifa 3498838, Israel;1. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, PR China;2. College of Information Science and Engineering, Ocean University of China, Qingdao 266071, PR China;3. Department of Engineering, Faculty of Technology and Science, University of Agder, N-4898 Grimstad, Norway;1. Department of Mechanics and Mathematics, Moscow State University, Vorobyovy Gory, 119992, Moscow, Russia;2. ICTEAM Institute, Université catholique de Louvain, 4 avenue Georges Lemaitre, B-1348 Louvain-la-Neuve, Belgium |
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| 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. |
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| Keywords: | Singular delta operator systems D-admissibility State feedback Lipschitz nonlinear perturbation Globally exponential stability |
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