Controllability of linear discrete systems in a Banach space. II (Q2703850)

Linear, discrete-time, infinite-dimensional control systems with constant coefficients are considered. It is generally assumed that the spaces of states and controls are infinite-dimensional real Banach spaces. The main purpose of the paper is to investigate local and global null-controllability in a given time interval and approximate null-controllability in a given time interval. Using the spectral theory of linear operators in Banach spaces several conditions for different types of controllability are formulated and proved. Relations between different kinds of controllability are also investigated. Moreover, many remarks and comments concerning controllability problems for infinite-dimensional control systems are presented. It should be pointed out that controllability problems of infinite-dimensional control systems have been recently considered in the monograph [\textit{J. Klamka}, ``Controllability of dynamical systems'', Kluwer (1991; Zbl 0732.93008)].