Stabilization and Setpoint Tracking for a Class of Systems with Matched and Unmatched Perturbations

Abstract

This article is concerned with the robust control of a class of uncertain systems with linear nominal part and perturbations which are of two kinds: matched and unmatched. A specific variant of Integral Sliding Mode Control (iSMC) is employed to systematically derive robust controllers for the specific class of systems for both stabilization and setpoint tracking objectives. The linear part of the composite controller employs mature linear control tools, while its nonlinear part is a nonlinear state feedback with “unit control” structure depending on the sliding surface and the uncertainty bounds. It is shown that an optimal selection of the sliding surface and the consequent selection of the nonlinear gain multiplying the “unit control” action, guarantee that sliding mode is achieved after a finite time interval despite the presence of unmatched perturbation. After entering sliding mode, the matched perturbations are fully rejected while the unmatched ones are non amplified. The numerical examples demonstrate the proposed methodologies on a single input nominally unstable plant.