Abstract
In this paper, finite-time incremental stability (FTIS) and finite-time incremental boundedness (FTIB) are investigated for nonlinear switched systems (NSS) with unstable systems. Firstly, based on the reverse mode-dependent average dwell time (MDADT) method, we propose some sufficient conditions for FTIS of NSS. Secondly, the sufficient conditions for NSS to be FTIB with an incremental performance index are given by the multiple incremental Lyapunov functions. Finally, a distinctive advantage of reverse MDADT method is that each subsystems satisfies FTIB in the activation interval. A example has been provided to show the effectiveness of the theoretic results developed.
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This work was supported by the Natural Science Foundation of Hebei Province (Grant A2021204004; A2022204001), Talents Introduction Project of Hebei Agricultural University (Grant YJ2020036; PY2021003), Youth Fundation project of Hebei Educational Committee (Grant QN2021080), Humanities and Social Sciences Youth Foundation, Ministry of Education of the People’s Republic of China (Grant 20YJC630001).
Lijuan Wang received her M.S. degree in applied mathematics from North China Electric Power University in 2009. She is currently an Associate Professor with Hebei Agricultural University. Her current research interests include switched systems and stochastic systems.
Yuanhong Ren received his Ph.D. degree in operations research and cybernetics from the Nanjing University of Science and Technology in 2020. He is currently an Associate Professor with Hebei Agricultural University. His current research interests include control theory of nonlinear switched and stochastic systems.
Yushi Yang is currently an Associate Professor in mathematics with the College of Science, Hebei Agricultural University. His research interests include applications of statistical, with current emphasis on incremental stability analysis and discrete-time systems.
Lin Guan received her M.S. degree in probability and statistics from North University of China in 2007. She is currently a Lecturer with Hebei Agricultural University. Her current research interests include multivariate statistics and control theory of stochastic systems.
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Wang, L., Ren, Y., Yang, Y. et al. Finite-time Incremental Stability Analysis for Nonlinear Switched Systems With Unstable Subsystems. Int. J. Control Autom. Syst. 21, 3166–3175 (2023). https://doi.org/10.1007/s12555-022-0137-1
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DOI: https://doi.org/10.1007/s12555-022-0137-1