Design and synthesis of piecewise-linear fuzzy systems

The main advantages of piecewise linear approximations are the availability of mature and precise analysis methods, and their suitability for simple hardware implementations. The control surface of a large number of practical fuzzy controllers is well approximated by means of PWL functions. In this work a design methodology for PWL fuzzy controllers is presented. As an example, the development of a two-input single-output fuzzy controller is presented and its stability in the phase plane is investigated. The closed-loop system trajectories in the phase plane are simulated and the system stability is assured by means of a globally quadratic Lyapunov function. In addition, two efficient hardware implementations are presented.