The elaboration of a stability theory of fuzzy systems is fully justified by the use, in a variety of practical situations, of fuzzy controllers [ 11, 27, 28). However, such a theory may be founded upon ideas that arise from a historical study of dynamical systems theory. During the last quarter of the nineteenth century, the study of ordinary differential equations underwent some rather radical changes. Prior to this period, the major emphasis in the subject had been on the methods of solving equations. It was during this period that Peano [20] gave a rigorous proof of the existence theorem for solutions of ordinary differential equations. During the same period, Lipschitz [ 151 and Picard [22] showed that the method of successive approximations led to a proof of the existence and the uniqueness of solutions to the initial value problem. These developments represent the dhuement of the attempts to solve differential equations. As the works of Peano, Lipschitz and Picard were finishing one chapter in the book of differential equations, another was being initiated with the research of Liapunov [ 141 and Poincare [23]. This new chapter was based on an entirely different approach, where one did not attempt to compute the solutions; rather one tried to exploit their topological properties. Poincart, in his famous m&moire [23], was the first to look at an ordinary differential equation from the point of view of the geometry of the trajectories, thereby creating the topological theory of ordinary differential equations. Almost at the same time, the stability theory created by Liapunov [ 141 although heavily quantitative in its methods, stressed the importance of some topological features of ordinary differential equations. During the 50 years following Liapunov and Poincare, many important advances were made. It is with the works of Birkhoff [4], Nemytskii and Stepanov [ 191, and Smale [26] that researchers realized that the essence of this theory was based on the notion of dynamical system. Based on Liapunovâs original works, âclassicalâ stability theory is concerned with the equilibrium points of the system and the dynamical