DETERMINATION OF THE TRANSITIVITY OF BILINEAR SYSTEMS

A well-known Lie algebra condition for controllability and accessibility of a bilinear system is considered. The possibility is considered of developing algorithms involving only rational computaions on the matrices, which would determine whether the rank condition is everywhere satisfied, i. e. whether the bilinear system has the accessibility or, in some instances, controllability property. It is shown that there do exist various sequences of rational operations on the matrices A//0,A//1, . . . , A//r which enable one in a finite number of steps to decide whether or not the system has the accessibility-transitivity property.