Stabilization and controllability of first-order integro-differential hyperbolic equations

Stabilization and controllability of first-order integro-differential hyperbolic equations

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prov...

Backstepping Boundary Control of First-order Coupled Hyperbolic Partial Integro-differential Equations

Abstract: We consider a feedback control problem of first-order coupled hyperbolic partial integrodifferential equations with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied under zero boundary inputs. Then, we apply a backstepping method to the design of the boundary inputs. Our main result shows that, for any initial data ...

Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

Impulsive Boundary-value Problems for First-order Integro-differential Equations

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y′(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t ∈ J0, ∆y(tk) = Ik(y(tk)), k = 1, 2, . . . , p,

On Exact Controllability of First-Order Impulsive Differential Equations