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 ( DELTA , X), whether DELTA is a GCI of X is introduced, and through it, a verdict of the solvability of the controlled invariance problem (CIP) is reached.