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Divergent Stability Conditions of Dynamic Systems

  • Nonlinear Systems
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Abstract

A new method for analyzing the stability of dynamic systems using the properties of the flow and divergence of the phase vector is proposed. A relation between Lyapunov’s function method and this method is established. Based on the results obtained below, a design procedure of state feedback control laws for stabilizing dynamic systems is developed. The control law design is reduced to solving a differential inequality with respect to the control function desired. Examples illustrating the applicability of the new and existing methods are considered.

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Acknowledgments

The results of Section 2 were obtained under support of the Russian Foundation for Basic Research in IPME RAS, project no. 17-08-01266. The results of Section 3 were obtained under support of the Russian Science Foundation in IPME RAS, project no. 18-79-10104.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    I. B. Furtat

  2. ITMO University, St. Petersburg, Russia

    I. B. Furtat

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  1. I. B. Furtat
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Correspondence to I. B. Furtat.

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This paper was recommended for publication by L.B. Rapoport, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 2, pp. 62—75.

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Furtat, I.B. Divergent Stability Conditions of Dynamic Systems. Autom Remote Control 81, 247–257 (2020). https://doi.org/10.1134/S0005117920020058

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  • DOI: https://doi.org/10.1134/S0005117920020058

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