Integral Sliding Manifold Design for Linear Systems With Additive Unmatched Disturbances

Abstract

This note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances. System sensitivity upon an unmatched disturbance vector is assessed by the steady-state dependent criterion function. The derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion. Applicability of this method in case of slowly-varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance. The proposed approach has been demonstrated on a numerical example and verified by simulations.