Abstract
This paper addresses the state-dependent stability problem of switched positive linear systems. Some exponential stability criteria are established on the given partitions of the nonnegative state space. First, a exponential stability of systems without delays is established with the help of a single linear co-positive Lyapunov function. When this does not seem possible, we also prove the stability by using multiple linear co-positive Lyapunov functions. Moreover, we extend this result to the delayed systems in terms of the single and multiple linear co-positive Lyapunov functionals respectively. The proposed results can be applied to the general systems without any special restriction. Some numerical examples are given to illustrate the effectiveness of our results.
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Recommended by Associate Editor Do Wan Kim under the direction of Editor Yoshito Ohta. This work was supported by the Foundation of National Nature Science of China (Grant No.61473239) and supported by the Fundamental Research Funds for the Central Universities (Grant No.2682014BR038 and 2682015CX058).
Xiuyong Ding is a senior lecturer of the School of Mathematics at Southwest Jiaotong University in Chengdu, China. He received his M.S. and Ph.D. degrees in Applied Mathematics from University of Electronic Science and Technology of China, in 2009 and 2012, respectively. His research interests include differential equations, hybrid systems and its applications.
Xiu Liu is a senior lecturer of the School of Mathematics at Southwest Jiaotong University in Chengdu, China. She received her M.S. and Ph.D. degrees in Applied Mathematics from University of Electronic Science and Technology of China, in 2010 and 2013, respectively. Her research interests include switched systems, impulsive systems, and descriptor systems.
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Ding, X., Liu, X. Stability analysis for switched positive linear systems under state-dependent switching. Int. J. Control Autom. Syst. 15, 481–488 (2017). https://doi.org/10.1007/s12555-015-0372-9
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DOI: https://doi.org/10.1007/s12555-015-0372-9