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. | |