Search

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.

This paper extends to H ∞ performance design a recent local approach for non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models based on the fuzzy Lyapunov function (FLF). The main obstacle for using FLFs altogether with TS models consists in handling the time-derivatives of the membership functions (MFs). By reducing global stability goals via local considerations, the aforementioned impediment has been removed leading to stabilization domains where H ∞ disturbance rejection is guaranteed. Conditions are expressed as linear matrix inequalities (LMIs), thus enabling systematic and efficient solutions which are solved by convex optimization techniques.