Abstract
This paper is concerned with nonlinear sliding mode and nonlinear regularization of piecewise smooth system. First, we give conditions to ensure that piecewise smooth system has a sliding periodic orbit with the sliding motion defined by Jeffrey’s nonlinear method. Then, nonlinear regularization of piecewise smooth system with a sliding periodic orbit will be discussed. We shall discuss two cases of this problem, i.e. planar case and higher dimension case. For each case, we establish sufficient conditions to ensure that the existence of periodic orbit for the regularized system. Moreover, we prove that the periodic orbit of regularized system will remain close to the sliding periodic orbit of the original piecewise smooth system as the small regularization parameter goes to 0.
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Acknowledgements
This work was partially supported by Natural Science Foundation of Fujian Province under Grant 2022J01307, Cultivation Program for Outstanding Young Scientific talents of Fujian Province in 2017 and Natural Science Foundation of China under Grant 12271096.
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Chen, X., Pi, D. Nonlinear Sliding and Nonlinear Regularization of Piecewise Smooth System. Qual. Theory Dyn. Syst. 22, 33 (2023). https://doi.org/10.1007/s12346-022-00705-8
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DOI: https://doi.org/10.1007/s12346-022-00705-8