Estabilização Paralela Distribuída de Sistemas Nebulosos de Takagi-Sugeno Utilizando Funções de Lyapunov Polinomiais Homogêneas no Estado

Abstract

This paper proposes an iterative algorithm based on linear matrix inequalities (LMIs) for the synthesis of state feedback controllers through distributed parallel compensation of Takagi-Sugeno fuzzy systems using homogeneous polynomial on the state Lyapunov functions. The proposed technique explores LMI conditions where the state-feedback gains appear linearly, so they can be treated directly as decision variables of the optimization problem, allowing the imposition of magnitude limitations on the gains in a straightforward way. The use of the decay rate as an objective function for the designed controller is also an immediate extension of the iterative algorithm, since it employs a relaxation directly related to such performance criterion. Numerical examples are used to compare the proposed method with another technique available in the literature based on quadratic Lyapunov functions, demonstrating the advantages of the proposed approach.