Accepted for publication in JNEEA

Controllability of Discrete Semilinear Impulsive Systems and Applications


C. Duque

Universidad de Los Andes, Departamento de Matematicas, Mérida 5101-Venezuela

H. Leiva

Yachay Tech, School of Mathematical Sciences and Information Technology, San Miguel de Urcuqui, Imbabura-Ecuador

J. Uzcátegui

Universidad de Los Andes, Departamento de Matematicas, Mérida 5101-Venezuela

Received on October 5, 2016, Revised version: November 7, 2016.
Accepted on November 20, 2016

Communicated by Martin Bohner

Abstract.  For many control systems in real life, impulses are intrinsic properties that do not modifytheir controllability. So we conjecture that under certain conditions the abrupt changes as perturbations of a system do not modify certain properties such as controllability. In other words, the controllability is robust by looking the impulses as perturbations. In this regard, here we prove the exact controllability and the approximate controllability of a semilinear difference equation with impulses. We prove that, under some conditions on the nonlinear term and the impulses, the exact controllability and the approximate controllability of the linear equation are preserved. Finally, we apply this result to a discrete version of the semilinear heat and wave equations.
Keywords: Difference equations, exact and approximate controllability, impulsive systems, heat and wave equation.
2010 Mathematics Subject Classification:   93B05, 93C25.

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