State bounding estimation of positive singular discrete-time systems with unbounded time-varying delays |
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| Institution: | 1. Faculty of Fundamental Science, Hanoi University of Industry, Bac Tu Liem District, Hanoi, Vietnam;2. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;3. Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, Vietnam;4. Department of Mathematics and Informatics, Thai Nguyen University of Science, Thai Nguyen, Vietnam;1. Department of Automation, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China;2. Shanghai Key Laboratory of Power Station Automation Technology, Shanghai 200444, China;1. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, China;2. School of Mathematics, Southeast University, Nanjing 210096, China;3. Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea;4. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China;2. Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province, Chengdu 611731, China;3. School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China |
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| Abstract: | This paper investigates the problem of state bounding for linear positive singular discrete-time systems with unbounded time-varying delay. Our approach is based on the comparison principle and the spectral analysis of matrices. Using the proposed approach, we provide new sufficient conditions for the regularity, causality, positivity and the existence of the smallest ultimate upper bound of such systems. The conditions are given in terms of linear programming problems, which can be solved by LP optimal toolbox. Numerical examples with simulation are given to demonstrate the advantage and validity of the proposed theoretical results. The proposed method is the first trial in the state bounding problem of linear singular discrete-time systems with unbounded time-varying delays. |
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