Robust Visual-Feedback Controller for Cart-Driven Pendulum with Fictitious Parameters and Parameter-Dependent Lyapunov Functions

This note addresses the robust visual-feedback controller design problem for a cart-driven pendulum using distorted images. This topic has already been addressed by several researchers; however, the adopted methods in the literature are conservative with respect to the freedom for designing controllers and/or the parameter-dependency of the Lyapunov functions. We therefore extend the design method using fictitious parameters and constant Lyapunov functions in the literature to the counterpart one using fictitious parameters and parametrically dependent Lyapunov functions. Thanks to the use of parametrically dependent Lyapunov functions, the proposed method is guaranteed to be no more conservative than the methods in the literature. We demonstrate the conservatism reduction of our proposed method compared to the method using fictitious parameters and constant Lyapunov functions for the design problem of robust visual-feedback controllers for the cart-driven pendulum. The design results as well as the experimental results are included to illustrate our contributions.