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

  • Volodymyr V. Pichkur
Part of the Understanding Complex Systems book series (UCS)


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.


Practical Stability Differential Inclusions Maximal Set Optimal Lyapunov Function Initial Conditions Representation 
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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Volodymyr V. Pichkur
    • 1
  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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