Structure of controllable positive integer autonomous linear discrete-time systems with scalar control (Q1386919)

Linear, autonomous, discrete-time, finite-dimensional, scalar input control systems are considered. Under the general assumption that the control system is positive and integer, algebraic properties of the attainable sets are discussed. Using algebraic methods, several conditions for controllability or reachability in a finite number of steps are formulated and proved. Special attention is paid to null-controllability in a finite number of steps. Finally, a simple illustrative example is presented. Moreover, many remarks and comments concerning the relations between different concepts of controllability and reachability are given. The results of the paper extend to the case of integer discrete-time systems, the controllability theorems presented in the papers [\textit{M. P. Fanti}, \textit{B. Maione} and \textit{B. Turchiano}, Int. J. Control 50, No. 6, 2523-2542 (1989; Zbl 0694.93003) and ibid. 51, No. 6, 1295-1308 (1990; Zbl 0702.93012)].