An LMI approach for second-order sliding set design using piecewise Lyapunov functions

This paper pursues recent results on second-order sliding set design for uncertain linear systems with matched uncertainties, a methodology that allows the designer to use a lesser number of derivatives; it is based on the direct Lyapunov method and its conditions are expressed as linear matrix inequalities, which are efficiently solved via convex optimization techniques. In contrast with former reports on this matter, the class of Lyapunov functions in this work is enlarged to the set of those which are piecewise C1, which naturally leads to design advantages as well as to a more natural adaptation of the Lyapunov function to the discontinuities arising in the sliding-set design methodology. Simulation examples are included to show the effectiveness of the proposed approach.