Finite Time Controllability of Nonlinear Control Processes

Abstract

A control process is globally finite time null controllable if it is globally asymptotically stable and locally controllable to the origin. Sufficient conditions are stated for the system \[\dot x = f(t,x,u)\quad {\text{in }}C^1 (R \times R^n \times R^m )\] to be globally finite time null controllable. The conditions are stated in terms of the Jacobian of f and the controllability of a related linear equation.