A necessary and sufficient condition for local constrained controllability of a linear system

The linear state equation is said to be locally Ω-null controllabe if, for every initial condition x0in some neighborhood of the origin, there exists a measurable control which steers x0to zero in finite time. The set Ω above is prespecified and corresponds to "actuator constraints" which depend on the underlying physical problem. This paper generalizes the known result of [1], i.e, our necessary and sufficient condition for local Ω-null controllability not only holds for the time-invariant systems considered in [1], but also holds for time-varying systems. The local controllability criteria given here complement a number of results given in [6], [7], [9]-[12] on global controllability.