Design of a fuzzy controller via fuzzy Lyapunov synthesis for the stabilization of an inertial wheel pendulum

In this paper was presented the design of a Mamdani type fuzzy controller to solve the stabilization problem for an inertial wheel pendulum. The fuzzy rule base are designed following the fuzzy Lyapunov synthesis, which guarantee the local asymptotic stability of the closed-loop system, by using a Lyapunov function whose time-derivative is negative semidefinite, while the use of heuristics is minimized in the design process. Moreover, the design of the fuzzy rule base is simplest than the hard task of solve the nonlinear differential equations traditionally used to model control systems. Deserves special emphasis the fact that the design is made without a mathematical model of the inertia wheel pendulum