New results on controllability of systems of the formẋ(t)= A(t)x(t)+f(t,u(t))

This paper presents new results on the so-called constrained controllability problem. Attention is focused upon the problem of steering the state
x(t)
of the system
\dot{x}(t)=A(t)x(t)+ f(t,u(t))
to a prescribed closed, convex target set
X
.The input
u(t)
is restricted to a prescribed compact set Ω. In contrast to the existing literature, our criteria for controllability require a much weaker set of hypotheses for their use, i.e., we dispense with traditional boundedness and positive invariance assumptions on the state transition matrix. Furthermore, we do not impose additional structure on the control set Ω and the target set
X
. Consequently, our results apply to a larger class of system than heretofore considered. In fact, we show that, under a strengthening of hypotheses, many of the existing results on constrained controllability follow directly from our theorems. From a computational point of view, our new controllability criteria appear to have one marked advantage over existing results: we do not have to search a subset of function space in order to ascertain whether or not a given system is controllable. Instead, we give criteria which involve only finite-dimensional spaces.