Behavioral Controllability of Delay-Differential Systems

Fixed Points and Controllability in Delay Systems

Schaefer’s fixed point theorem is used to study the controllability in an infinite delay system x′(t)=G(t,xt) + (Bu)(t). A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system x′(t) = λ[G(t,xt) + (Bu)(t)], 0 < λ < 1, then there exists a solution for λ = 1. The a priori bound is established by mean...

Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

In this manuscript, we have a tendency to execute Banach contraction fixed point theorem combined with resolvent operator to analyze the exact controllability results for fractional neutral integrodifferential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. An illustration is additionally offered to exhibit the achieved hypotheses.

Controllability of Damped Second-Order Neutral Impulsive Stochastic Functional Differential Systems with Infinite Delay

In this paper we study the controllability of damped second order neutral impulsive stochastic functional differential system with infinite delay in Hilbert spaces. Sufficient conditions for controllability results are obtained by using the theory of cosine families of bounded linear operators and fixed point technique. An example is provided to illustrate the theory.

Approximate Boundary Controllability for Semilinear Delay Differential Equations

Existence and Controllability Results for Damped Second Order Impulsive Functional Differential Systems with State-dependent Delay

Abstract. In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provide...