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Lyapunov Theory for Dynamic Equations

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Stability Theory for Dynamic Equations on Time Scales

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

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Abstract

In the present, the direct method of motion stability analysis is extended for a number of classes of equations involved in the description of many natural processes and phenomena. Depending on the type of auxiliary functions used (scalar, vector, or matrix), the initial system is transformed by means of a Lyapunov function into a system (scalar, vector, or matrix) which can be more suitable for stability analysis of solutions than the initial one. The class of dynamic equations includes time-continuous and time-discrete systems and allows to describe the processes in which the continuous and the discrete components are of equal importance for the formation of a general dynamic property of the process (motion). Therefore, a problem of the direct Lyapunov method generalization for dynamic equations is both of theoretical and practical interest. This chapter contains the results obtained in this direction of the stability theory developed basing on the ideas of the direct Lyapunov method.

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Authors and Affiliations

  1. National Academy of Sciences of Ukraine, Kiev, Ukraine

    Anatoly A. Martynyuk

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  1. Anatoly A. Martynyuk
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Martynyuk, A.A. (2016). Lyapunov Theory for Dynamic Equations. In: Stability Theory for Dynamic Equations on Time Scales. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-42213-8_3

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