Numerical synthesis and analysis of robust discrete time feedback control for nonlinear systems with parametric uncertainties

A method of numerically determining discrete time state feedback control inputs for nonlinear systems in a canonical form with parametric uncertainties is proposed. This method is based conceptually on sliding mode control and may be implemented practically by performing intensive computations off line to create a lookup table used in real time. Methods for numerically analyzing the behavior of the closed loop system are developed and proposed. In particular, reasonable sufficient conditions are established for the exponential stability of the uncertain system. These conditions may be evaluated numerically in a practical manner. This analysis method is demonstrated in the analysis of the closed loop behaviour of a system with the aforementioned numerically synthesized control law applied. This analysis method may be applied to any discrete time control law that attempts to emulate a sliding controller by forcing the system state near to a target manifold.