Null controllability of semilinear integrodifferential systems in Banach space (Q1375857)

Semilinear abstract integrodifferential control systems with time-varying parameters and infinite delay are considered. It is assumed that the linear part contains an unbounded operator which is the infinitesimal generator of an analytic semigroup and the nonlinear part satisfies a Lipschitz type condition. Using a Schauder fixed point theorem, a sufficient condition for global null exact controllability in a given time interval is formulated and proved. As an illustrative example, null controllability of a partial integrodifferential control system with a uniformly elliptic linear part and a special form for the nonlinear part is discussed. Moreover, remarks and comments on controllability problems for semilinear abstract control systems are given. The purpose of the paper is to extend the results given in [\textit{K. Balachandran}, \textit{P. Balasubramaniam} and \textit{J. P. Dauer}, J. Optimization Theory Appl. 88, 61-75 (1996; Zbl 0848.93007)], to semilinear control systems with unbounded linear operators and infinite delay in the state variables.