Design of sliding mode controllers with actuators using Attracting Ellipsoid Method

The Attracting Ellipsoid Method is applied for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations. The control signal is applied to the system through a first order actuator whose time is to be designed to guarantee quasi-optimal practical stability at the same time that the control signal posses a sub-optimal amplitude. 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.