The problem is considered of steering the state of a linear time-varying system to the origin when the control is subject to magnitude constraints. Necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control (satisfying the constraints) which steers the system to the origin from a specified initial epoch (x//0 , t//0). The global result does not require zero to be an interior point of the control set OMEGA , and the theorem for constrained controllability at (x//0, t//0) only requires that OMEGA be compact, not that it contain zero. The results are compared to those available in the literature. Furthermore, numerical aspects of the problem are discussed as is a technique for determining a steering control.
