Novas funções de Lyapunov Fuzzi e soluções numéricas para análisede estabilidade e controle de sistemas via modelagem Takagi-Sugeno: aproximando os controles fuzzi e não-linear

Abstract

This addresses conservativeness in stability analysis and fuzzy control design of dynamic systems in Takagi-Sugeno form. The emphasis in on new parameterized Lyapunov functions and in the search and development of solutions to recast the analysis and synthesisconditions into the framework of Linear Matrix Inequalities. Such systems are of great interest because a large family of nonlinear dynamics can bemodelled, approximately or exactly, in compact domains, by means of a combination of linear models locally valid interpolated with membership functions. In this way nonlinear systems can be treated with the formalism of gain-scheduling control, combining several numerical tools dedicated for linear systems, allowing numerical solutions for the controlproblem that are scalable and sytematic. This is a great advantage in comparison with the formalism present in direct nonlinear control, by means of techniques such as feedback linearization and backstepping, in which the solutions are customized for each control problem. The price paid for the less complex design procedure is more conservativeness,resulting in worst performances or even unfeasibility. Progressively, Takagi-Sugeno systems have been seen less and less as simply multimodel systems with strong polytopic characteristic being relevant nowadays take into account they time-varying and nonlinear features. This work intends to contribute in this sense by proposing new Lyapunov functions that are able to better characterize these relevant properties of fuzzy systems. Another contribution is propose and investigate numerical solutions that reduce conservativeness as the the computational demand is kept low when the task is to recast the analysis and synthesis conditions into the framework of Linear Matrix Inequalities. In short, this thesis tries to bring together the nonlinear and fuzzy fields by means of less conservative methodologie.