Nonquadratic Controller and Observer Design for Continuous TS Models: A Discrete-Inspired Solution

This work deals with controller and observer design for continuous-time Takagi-Sugeno models based on a new nonquadratic Lyapunov function. The proposed technique intends to attain the level of development reached by its discrete-time counterpart by suitably adapting one of its key ideas: the inclusion of former values of the premise variables. The proposed approach naturally overcome the problem of dealing with the time-derivatives of the membership functions, thus providing a simplified as well as easier alternative to recent results on this matter. Moreover, thanks to the Finsler's Lemma and a Tustin-like transformation, controller and observer gains are decoupled from the proposed Lyapunov function. The results are expressed as linear matrix inequalities which are efficiently solved by commercially available software implementing convex optimization techniques.