Necessary and sufficient conditions for the target set of nonlinear infinite space of neutral functional differential systems with distributed delay in the control to be on the boundary of the attainable set

Abstract

In this paper, Nonlinear infinite space of Neutral Differential Systems with Distributed Delays in the Control of the form d/dt [D(t,xt)] = L(t,xt)xt + ∫0-∞ A(t,θ)х(t+θ)dθ + f(t,xt) + ∫0-h  (dθH(t,θ)u(t+θ) is presented for the study. The system was linearized and integrated to obtain a
solution. The unsymmetric Fubini theorem was used) to obtain an expression for the solution. The set functions upon which our study hinges were extracted. The necessary and sufficient conditions for the target to be on the boundary of the attainable set were established.