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Parallelisms between differential and difference equations

Veronika Chrastinová, Václav Tryhuk (2012)

Mathematica Bohemica

The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.

Partial generalized synchronization theorems of differential and discrete systems

Jianyi Jing, Lequan Min, Geng Zhao (2008)

Kybernetika

This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.

Perfect observers for fractional discrete-time linear systems

Ewa Pawluszewicz (2016)

Kybernetika

A perfect (exact) fractional observer of discrete-time singular linear control system of fractional order is studied. Conditions for its existence are given. The obtained results are applied to the detectability problem of the class of systems under consideration.

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