DESIGN OF STABILIZING CONTROL LAWS FOR SMOOTH NONLINEAR-SYSTEMS

A simple design procedure is presented for determining a continuous, stabilizing control law for a class of non-linear single-input systems. The design procedure uses state-feedback transformation which approximately linearizes the non-linear system. A robust controller is then designed and shown to stabilize the system locally, despite a non-linear additive error term. The size of the region in the state space in which the controller stabilizes the system is shown to depend on parameters reflecting the 'speed of variation' of the non-linear system.