Analysis and design of switched normal systems |
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| Institution: | 1. Department of Mechanical Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Sakai, Osaka 599-8531, Japan;2. Department of Electrical and Computer Engineering, Penn State Erie, Benson 182, 5091 Station Road, Erie, PA 16563-1701, USA;3. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA;1. School of Astronautics, Beihang University, Beijing 100191, China;2. School of Instrument Science and Opto-electronics Engineering, Beihang University, Beijing 100191, China;1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China;2. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway |
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| Abstract: | In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate. |
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