Analysis and design of integral sliding manifolds for systems with unmatched perturbations

The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H_∞ is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.