Control Design for Uncertain Systems Based on Integral-Type Sliding Surface

An advanced robust sliding mode control scheme is proposed for linear systems. First, based on LMI technique the positive definite matrix which is key to construct the sliding surface is found , then a global integral-type sliding surface is constructed for the systems in the presence of both matched and unmatched uncertainties, then the global sliding mode controller is constructed for systems both with matched and unmatched uncertainties. In terms of LMIs the sliding surface is easy to design especially for even large-scale systems in the computational aspect. Furthermore the controlled system during ideal sliding mode completely nullifies matched uncertainties and inherits the same properties as those of the controlled nominal system in the absence of uncertainties. In addition, since the reaching phase is eliminated, the controlled system is more robust against perturbations than the other variable structure control system with reaching phase.