RELATIVE CONTROLLABILITY OF NEUTRAL FUNCTIONAL INTEGRODIFFERENTIAL SYSTEMS IN ABSTRACT SPACE WITH DISTRIBUTED DELAYS IN THE CONTROL

Abstract

In this paper, Abstract Neutral Functional Integrodifferential System with Distributed Delays in the control was presented for relative controllability analysis. We used variation of parameters to obtain the solution of our system of interest as an integral equation. The integral equation contains the values of the control  .The values of the control u(t) for  enter into the definition of the initial complete state. To separate them we applied the Unsymmetric Fubini Theorem and the integration is in the Lebesque-Stielties sense. The set functions (controllability grammian, reachable set, attainable set, target set) upon which our study hinges were extracted and thus established that the system is relatively controllable. However, necessary and sufficient conditions for the relative controllability of the system were stated and established/proved.