On the stability and uniform stability of retarded integro-differential equations
Cemil Tunç, Sizar Abid Mohammed · Alexandria Engineering Journal · 2018
In this paper, the authors obtain new sufficient conditions for stability (S) and uniform stability (US) of solutions of the first order retarded Volterra integro-differential equations (VIDEs) in the formx′=A(t)x+∫t-τtC(t,s)ϕ(s,x(s))ds+f(t,x,x(t-τ)). The analysis of the obtained (S) and (US) results mainly depend on the definition of an appropriate Lyapunov functional (LF). An example is provided to illustrate the effectiveness of the proposed results. MATLAB-Simulink is applied to show the behaviors of the paths of solutions of the considered (VIDEs) for a particular case.