Stability analysis of a class of nonlinear positive switched systems with delays |
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| Institution: | 1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China;2. Institute of Automation, Qufu Normal University, Qufu, Shandong 273165, China;1. School of Mathematical Sciences, University of Jinan, Jinan, Shandong Province, 250022, China;2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong Province 266590, China;3. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong Province 273165, China;1. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China;2. Key Lab for IOT and Information Fusion Technology of Zhejiang, Hangzhou Dianzi University, Hangzhou 310018, China;3. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;4. College of Mathematics, Physics, and Information Engineering, Zhejiang Normal University, Jinhua 321004, China |
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| Abstract: | This paper addresses the stability problem of delayed nonlinear positive switched systems whose subsystems are all positive. Both discrete-time systems and continuous-time systems are studied. In our analysis, the delays in systems can be unbounded. Two conditions are established to test the local asymptotic stability of the considered systems. The method to compute the domains of attraction is also proposed provided that the system is locally asymptotically stable. When reduced to general nonlinear positive systems, that is, the considered switched system consists of only one mode, an interesting conclusion follows that the proposed nonlinear positive system is locally asymptotically stable for all admissible delays and nonnegative nonlinearities which satisfy an extra condition at the origin, if and only if the system represented by the linear part is asymptotically stable for all admissible delays. Finally, a numerical example is presented to illustrate the obtained results. |
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| Keywords: | Delays Nonlinear systems Positive systems Stability Switched systems |
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