Robustness of static sliding mode control for non-linear systems

Abstract

Robustness of static sliding mode control based on affine non-linear state space models in regular form is considered. This is necessary because the stability of non-linear systems is usually a local property which can be destroyed by an additive uncertainty. Thus the uncertainty should be appropriately structured. A cone bounded uncertainty structure is assumed in this paper. In general, when a regular form is used to design a static sliding mode control, only matched uncertainty can be expelled. For the stability of the closed-loop system, a minimum phase assumption is necessary. It is shown that the sliding manifold is equivalent to the manifold determined by the zero dynamics and the minimum phase assumption relates to the compactness of the sliding manifold in the ideal sliding mode. It is also shown that the two phase separability, i.e. reaching mode and ideal sliding mode, which holds for linear systems, does not hold generally for non-linear systems. A pertinent example is given.