A dual design problem via multiple Lyapunov functions

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

“…Our approach is based on two assumptions. The first one relies on the existence of a proportionality relation between multiple quadratic Lyapunov functions, and the second one considers an upper bound to the time derivative of the premise membership function as assumed by Tanaka et al (2001a;2001b;2001c;. Simulation examples demonstrate the effectiveness of our approach even for systems that do not admit a quadratic stabilization.…”

“…In this context, new stability conditions for TakagiSugeno fuzzy models are derived in this paper, based on the use of multiple Lyapunov functions that have been discussed (Cao et al, 1997;Chadli et al, 2000;Hadjili, 2002;Jadbabaie, 1999;Tanaka et al, 2001a) due to their properties of conservatism reduction. It is demonstrated that sufficient conditions for the stability and performance of a system are stated in terms of the feasibility of a set of Linear Matrix Inequalities (LMIs) (Boyd et al, 1994;Tanaka and Sugeno, 1992;Tanaka et al, 2001c), where the problem can be numerically solved by convex optimization techniques.…”

Continuous quasi-LPV Systems: how to leave the quadratic Framework?

“…Nonetheless, the quadratic approach presents serious limitations because its solutions are inherently conservative, i.e., there are stable or stabilizable models which do not have a quadratic solution , this conservativeness comes from different sources : the type of T-S model , , the way the membership functions are dropped-off to obtain LMI expressions [Tuan & al, 2001], , 2007a, the integration of membership-function information [Sala & Guerra, 2008], , or the choice of Lyapunov function [Johansson & al, 1999], [Tanaka & al, 2001c], there was room for reducing this conservativeness by changing the choice of the Lyapunov function.…”

“…In other approaches, it is taking in consideration the upper bound for the time derivative of the premise membership function as assumed by [Tanaka & al, 2001a[Tanaka & al, , 2001c[Tanaka & al, , 2003.…”

“…Several studies using this type of functions either in the continuous case [Jadbabaie & al, 1999], [Morère, 2001], [Blanco et al, 2001], [Tanaka et al, 2001c], or in the discrete case [Morère, 2001], [Kruzewski & al, 2008].…”