Piecewise affine model and control of bicycle by gyroscopic stabilization

This paper considers the naturally unstable unmanned bicycle system at constant forward and rotational speeds. The bicycle is attached with a gyroscopic flywheel acting as an actuator for roll angle stabilization. The nonlinear model of the system is approximated by piecewise affine functions which minimizes the model error even outside the operating regions. The controller synthesis problem is cast as Linear Matrix Inequalities problem. The feasible control law is derived based on quadratic Lyapunov function to guarantee the system stability for all regions. The simulation confirms the effectiveness of this approach.