CONTROLLABILITY PROPERTIES OF CONSTRAINED LINEAR-SYSTEMS

In this paper, we present results on constrained controllability for linear control systems. The controls are constrained to take values in a compact set containing the origin. We use the results on reachability properties discussed in Ref. 1. We prove that controllability of an arbitrary point p in R(n) is equivalent to an inclusion property of the reachable sets at certain positive times. We also develop geometric properties of G, the set of all nonnegative times at which p is controllable, and of C, the set of all controllable points. We characterize the set C for the given system and provide additional spectrum-dependent structure. We show that, for the given linear system, several notions of constrained controllability of the point p are the same, and thus the set C is open. We also provide a necessary condition for small-time (differential or local) constrained controllability of p.