Equivalence of several characteristics of dual switched linear systems |
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| Institution: | 1. Department of Automation, School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China;2. Shanghai Key Laboratory of Power Station Automation Technology, Shanghai 200072, China;3. Department of Engineering and Design, University of Sussex, Brighton, BN1 9QT, UK;4. School of Information, Zhengzhou University, Zhengzhou 450052, China |
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| Abstract: | This paper is concerned with the equivalence of several dynamic characteristics between mutually dual switched linear systems, both discrete- and continuous-time cases are considered. Two systems are mutually dual means that their system matrices are transpose of each other. The dynamic properties considered in this paper include four types: exponential stability, global uniform asymptotic stability, attractivity, and weak attractivity. It is shown that every one of the four dynamic properties of a switched linear system implies each of the four dynamic properties of its dual system, and vice versa. The main results enable us to investigate these dynamic properties of switched system by virtue of study related to the corresponding properties of its dual system, thus providing an alternative way to explore the dynamics of switched systems. A numerical example is provided to illustrate the obtained theoretical conclusions. |
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| Keywords: | Attractivity Dual systems Global uniform asymptotic stability Homogeneous systems Switched linear systems |
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