Feedback Implementability of Sliding Modes in Nonlinear Control Systems

Abstract We consider general multivariable control systems, described by nonlinear ordinary differential equations. Given any sliding manifold in the state space and any ideal sliding motion on it, we find an explicit control algorithm which allows us to obtain, up to any fixed tolerance, the same dynamic behavior of the ideal motion by using the trajectories of a new control system, which is affine in the control variables, and is obtained by transforming the original one via a suitable switching logic. The affine dependence on the control variables guarantees the fulfillment of the approximability property, thereby extending the scope of the theory.