APPROXIMATE CONTROLLABILITY OF SECOND ORDER SEMILINEAR DELAY CONTROL SYSTEMS

Abstract

In this article, we investigate some sufficient conditions, for approximate controllability of an abstract second order semilinear delay control system of the form

x''(t) = Ax(t) + Bu(t) + f(t, x(t + \theta), u(t)),

where 0 < t <= T and -h <= \theta <= 0, using the theory of strongly continuous cosine families.
An example is provided to illustrate the theory.