Continuous Takagi–Sugeno's Models: Reduction of the Number of LMI Conditions in Various Fuzzy Control Design Technics

Abstract

Fuzzy models of the Takagi-Sugeno type enable representation of a wide class of nonlinear models. Conditions about their stabilization can be derived systematically. Usually these conditions are written as linear matrix inequality (LMI) problems. In this paper, we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws. We will work out with continuous fuzzy models, and supply results about the stabilization, the regulator problem, and also H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control. Solutions based on a reduced number of decision variables, implying a reduced number of LMI conditions, are also proposed. We show that a good tradeoff can been obtained.