Attracting Ellipsoid Method application to designing of sliding mode controllers

The Attracting Ellipsoid Method is applied for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations. The existence of first order actuators is considered and their time constants are designed to provide quasi-optimal practical stability. The technique is based on the existence of an attracting (invariant) ellipsoid such that the convergence to a quasi-minimal region of the origin is guaranteed. The design procedure is given in terms of the solution of a set of Linear Matrix Inequalities. A benchmark example illustrating the design is given.