Abstract
This paper considers the problem of controllability and observability of a linear dynamical system with combinatorial constraints imposed on its input and output terminals; especially, matroidal-type constraints are thoroughly studied. The problems of examining the controllability and observability under constraints of matroidal type are reduced to the problem of finding a maximum common independent set of two appropriately defined matroids. Effective constructive algorithms are presented for several typical matroidal constraints and the best upper bounds of the time are given in which the controllability and the observability are to be decided.
