Abstract
This paper investigates the input/output-to-state stable (IOSS) property of the switched systems under average dwell time (ADT) switching signals in two cases: 1) all of the subsystems are IOSS, 2) parts of the subsystems are IOSS, and proposes a number of new results on stability analysis. First, we present a new IOSS result for the switched nonlinear systems whose subsystems are IOSS with an improved ADT method. Second, extending the improved ADT method to unforced nominal switched nonlinear systems in which parts of subsystems are stable, we establish a new stability analysis result. IOSS property of switched nonlinear systems in which parts of subsystems are IOSS, we show that if the average dwell time is large enough and if the fraction of time where one of the non-IOSS system is active is not too big, then IOSS property of the switched system can be established. It should be pointed that the main results obtained in this paper have some advantages over the exiting ones. Finally, two illustrative examples with simulation verify the correctness and validity of our results.
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Recommended by Associate Editor Izumi Masubuchi under the direction of Editor Yoshito Ohta. This work is supported by National Natural Science Foundation of China [61374074, 61304133, 61305130,61473173], China Postdoctoral Science Foundation funded project [2013M541915,2014T70638] and the Scientific Research Foundation of Shandong province Outstanding Young Scientist Award [BS2013SF023].
Lixia Liu was born in Weifan, China in 1990. She received her B.S. degree in Mathematics from Qilu University of Technology, Jinan, China, in 2014. She is currently a graduate student for master degree. Her research interests include nonlinear systems, switched systems.
Rongwei Guo was born in Jinan, China in 1979. He received his B.S. degree in Mathematics from University of Jinan, Jinan, China, in 2001, and his M.S. and Ph.D. degrees in Mathematics of Shanghai University and Shandong University, China, in 2004 and 2011, respectively. He joined School of Science at Qilu University of Technology in 2004, where he is currently a professor. His research interests include nonlinear systems, switched systems.
Shuping Ma was born in Rizhao, China in 1970. She received her B.S. degree in Mathematics from Shandong University, Jinan, China, in 1992, and her M.S. and Ph.D. degrees in Mathematics and System Science of Shandong University, China, in 1997 and 2000, respectively. She joined School of Mathematics and System Science at Shandong University in 2000, where she is currently a professor. Her research interests include singular systems, time-delay systems, Markov jump systems, robust control.
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Liu, L., Guo, RW. & Ma, SP. Input/output-to-state stability of switched nonlinear systems with an improved average dwell time approach. Int. J. Control Autom. Syst. 14, 461–468 (2016). https://doi.org/10.1007/s12555-014-0292-0
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DOI: https://doi.org/10.1007/s12555-014-0292-0