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On the Problem of Nonlinear Stabilization of Switched Systems

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Abstract

The asymptotic stability and ultimate boundedness of the solutions for nonlinear switched systems is investigated. It is assumed that every mode of the system is unstable. The required behaviour of the switched system is achieved by using a special nonstationary coefficient, which can be considered as a multiplicative control. It is assumed that this coefficient is a piecewise constant function, and the value of the coefficient changes when the mode changes. Sufficient conditions on the coefficient are found to guarantee the asymptotic stability of the zero solution of the switched system or the ultimate boundedness of solutions with a given bound. These results are applied to the stability analysis of some classes of mechanical systems. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.

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Acknowledgements

This work was supported by the Russian Foundation of Basic Researches, Grant No. 16-01-00587.

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  1. Saint Petersburg State University, 7/9 Universitetskaya Nab., St. Petersburg, Russia, 199034

    A. V. Platonov

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Platonov, A.V. On the Problem of Nonlinear Stabilization of Switched Systems. Circuits Syst Signal Process 38, 3996–4013 (2019). https://doi.org/10.1007/s00034-019-01048-7

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