Matrix rank based conditions for reachability/controllability of dicrete linear repetitive processes
Linear, finite-dimensional, time-invariant discrete repetitive control systems are considered. Using the so-called 2-D representation of the repetitive processes the general response formula is given in terms of the transition matrix of a suitably defined 2-D discrete system. Next, necessary and sufficient conditions for controllability and reachability in a given domain are formulated and proved. These conditions require verification of rank conditions for suitably defined controllability and reachability matrices. Moreover, several remarks and comments on the relationships between different concepts of controllability and observability are given. The relationships to the results which are known in the literature are also discussed. Similar controllability and reachability problems for multidimensional discrete control systems have been recently considered in the monograph [\textit{T. Kaczorek}, Linear control systems. Vol. 1: Analysis of multivariable systems. New York: John Wiley \& Sons Inc. (1992; Zbl 0784.93002); Vol. 2: Synthesis of multivariable systems and multidimensional systems. New York: John Wiley \& Sons Inc. (1993; Zbl 0784.93003)].
scientific article; zbMATH DE number 1354711