Towards a global nonquadratic controller design for nonlinear systems via robust differentiators and Takagi-Sugeno models

This paper presents a novel solution for nonquadratic controller design of nonlinear systems via Takagi-Sugeno models; it employs a first-order Levant´s robust differentiator for finite-time exact estimation of the time derivatives of the membership functions, which appear as a consequence of the use of fuzzy Lyapunov functions. In contrast with most of the solutions on the subject, the proposed approach offers global instead of local conditions, do not require bounds on the time derivatives (which cannot be always available), and leads to linear matrix inequalities which do not depend on any extra parameters. Examples show that stabilization is achieved up to the differentiator finite-time convergence.