Region of acceptable motions

The mathematical problem of determining the set of initial conditions for which a given nonlinear control system is asymptotically stable in the sense of Liapunov has been the object of considerable research. The more practical problem of determining the set of initial conditions for which a given nonlinear control system is asymptotically stable and the trajectory remains within a given region of the state space is formulated mathematically. An approach to estimating the defined region of acceptable motions is indicated.