STABILITY ANALYSIS AND DESIGN OF FUZZY SYSTEMS USING PIECEWISE QUADRATIC APPROACH

Abstract

Fuzzy logic basically performs the mapping process which maps any variable from input space to the output space. While the design methodology for fuzzy controllers has proven itself in certain commercial and industrial applications, there is a significant need to perform mathematical analysis of fuzzy control systems prior to implementation: (i) to verify and certify their behavior so that instabilities can be avoided for applications demanding highly reliable operation such as aircraft and nuclear reactor control, and (ii) to provide insight to the expert on how to modify the fuzzy controller to guarantee that performance specifications are met. This process involves high level of complexity consequently the dynamical behavior of systems consisting fuzzy logic control may be much richer and complex than that of linear systems. The present dissertation work is a detailed study of stability analysis of fuzzy control systems with piecewise quadratic lyapunov functions .Construction of lyapunov functions is one of the most fundamental problems in system theory. The most direct application is stability analysis. A given nonlinear plant is represented by the Takagi — Sugeno fuzzy model. This fuzzy modeling method is simple and natural. The system dynamics is captured by set of fuzzy implications which characterize local relations in state space. The main feature of a Takagi-Sugeno Fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear model. The over all fuzzy model is achieved by fuzzy blending of the linear system models. Stability conditions are obtained which are basically mathematical expressions known as linear matrix inequalities. Matlab's lmilab toolbox is utilized for solving linear matrix inequalities.