On controlled invariance in nonlinear systems

The notion of Generalized Controlled Invariance (GCI) is introduced to allow for the loss of degrees of freedom in control that may be the necessary price for achieving a desired invariance. It is shown that subject to some technical rank restrictions, controlled invariance implies GCI. A sequential procedure that definitively establishes for a given system pair (Δ, χ), whether Δ is a GCI of χ is introduced, and through it, a verdict o the solvability of the controlled invariance problem (CIP) is reached.