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Maximum Sets of Initial Conditions in Practical Stability and Stabilization of Differential Inclusions

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Modern Mathematics and Mechanics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

In this work we consider the problem of practical stability of differential inclusion solutions on the basis of the maximum sets of practical stability concept. On one hand we propose results concerning nonlinear differential inclusion including both topological properties of the maximum sets of initial conditions for four types of practical stability (internal, weak internal, external, weak external) and the necessary and sufficient conditions of internal practical stability using the optimal Lyapunov function. On the other hand we offer the analytical forms of the maximum sets of initial conditions representation in the linear differential inclusion case. In the last section we consider the problem of practical stabilization.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Volodymyr V. Pichkur

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  1. Volodymyr V. Pichkur
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Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

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Pichkur, V.V. (2019). Maximum Sets of Initial Conditions in Practical Stability and Stabilization of Differential Inclusions. In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-96755-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-96755-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96754-7

  • Online ISBN: 978-3-319-96755-4

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