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Converse theorem for practical stability of nonlinear impulsive systems and applications

Boulbaba Ghanmi, Mohsen Dlala, Mohamed Ali Hammami (2018)

Kybernetika

The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of...

Convolution operators on spaces of holomorphic functions

Tobias Lorson, Jürgen Müller (2015)

Studia Mathematica

A class of convolution operators on spaces of holomorphic functions related to the Hadamard multiplication theorem for power series and generalizing infinite order Euler differential operators is introduced and investigated. Emphasis is placed on questions concerning injectivity, denseness of range and surjectivity of the operators.

Coordinate description of analytic relations

František Neuman (2006)

Mathematica Bohemica

In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.

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