On the uniform convergence of solutions to a control system of integral equations under the weak convergence of controls
We consider a control system of Volterra type integral equations, linear in the control, the integrand of which is measurable in the integration variable. We prove that if a sequence of controls converges weakly in $L_1$ space, then the solutions of the system for sufficiently far numbers exist and uniformly converge to the solution corresponding to the limit control.