Discrete Variable Structure Control for Linear Multivariable Systems: The Output Feedback Case

This paper presents an observer-based discrete variable structure controller for linear multivariable systems with unmatched additive uncertainties, an extension of the results reported in [12] to the output feedback case. It is shown that the incorporation of a prediction observer with uncertainty estimation into the controller guarantees the attractiveness and invariance of the estimated boundary layer, which is dynamic and parallel to the sliding hyperplane, after a transient. As in the state feedback case¹, linear control design strategies are applicable to the tracking error dynamics design inside the estimated boundary layer under an eigenvalue constraint. A numerical example is used to illustrate the proposed technique.