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Qualitative Analysis of Impulsive Equations

  • Anatoly A. Martynyuk
Chapter

Abstract

In recent years, the method of matrix Lyapunov-like functions, which is a generalization of the classical Lyapunov direct method based on matrix-valued functions, has been significantly developed (see, for example, Martynyuk [64, 66, 69] and the references therein). Parallel to the development of the method for different classes of new equations, the structure of the matrix-valued Lyapunov functions remains of great importance and attracts an increasing attention. It is well known that the components of the matrix-valued functions depend on the system of equations under consideration, as well as on compositions of its subsystems. A natural subject for the investigation by means of the multi-component Lyapunov-like functions with different components is the class of impulsive systems.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Anatoly A. Martynyuk
    • 1
  1. 1.Institute of MechanicsNational Academy of Sciences of UkraineKievUkraine

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