Abstract
This paper considers the reachability of discrete bilinear systems described by x(t+1)=Ax(t)+Nx(t)u(t)+bu(t) t=0, 1, 2, …, where u is scalar control. This problem has a solution when the control is bounded or rank [N, b]=1.
In this paper there is no such limitation on the control. First, the properties of the set of states reachable in t steps from a nonzero initial state are investigated. Next, a sufficient condition for the existence of initial states, from which any state in Rn can be reached in n steps, is presented. As a result the control sequence that transfers the initial state to any desired state can be obtained in an explicit way.
