A General and Formal Methodology to Design Stable Nonlinear Fuzzy Control Systems

The price to be paid for the great dynamic richness of nonlinear systems is the lack of a unitary theory that allows control-system design to be tacked in a way that is parallel or analogous to that of linear systems. We propose a general methodology that uses fuzzy logic to systematically and formally synthesize nonlinear control systems, which are stable by design. Although this methodology is based on Lyapunov theory, it avoids searching for Lyapunov functions. This allows the synthesis procedure to be systematic as well as formal and, especially, independent of heuristics. Some examples of nonlinear control are solved in this paper, thus allowing assessment of the proposed methodology.