On the controllability of singular systems in Banach spaces (Q1373114)

Linear, discrete-time, infinite-dimensional, stationary control systems are considered. Fundamental definitions of different kinds of controllability with constrained controls are given. Next, using the methods of functional analysis and specially theorems on linear bounded operators, a necessary and sufficient condition for global exact controllability with constrained controls is formulated and proved. The main tool of the proof is based on an extension of the surjectivity theorem to set-valued functions [\textit{S. M. Robinson}, Math. Oper. Res. 1, 130-143 (1976; Zbl 0418.52005)]. Moreover, several remarks and comments on controllability problems for discrete singular control systems are given. Finally, a simple numerical illustrative example is presented.