Sliding surface design via linear matrix inequalities and Finsler´s Lemma

This paper presents a novel sliding surface design for uncertain linear systems. The proposed approach is twofold inspired: on the one hand, it acknowledges the increasing interest of the sliding control community to formulate their problems in terms of linear matrix inequalities since they are efficiently solved via convex optimization techniques; on the other hand, it incorporates recent developments based on Finsler´s Lemma for Lyapunov-based design. It is shown that former results are included as particular cases of the new approach. Illustrative examples are provided.