Robust stabilization of the inertia wheel pendulum

A delayed state feedback law is presented to stabilize the inertia wheel pendulum, which guarantees the closed-loop system to be globally asymptotically stable in the presence of time delays. The inertia wheel pendulum is transformed into a 4-dimensional chain of integrators with higher order nonlinearity, and a saturated control law is provided with saturation level and time delay explicitly specified. The globally asymptotic stability of the closed-loop system is also proven in a simple way. Finally, simulation results show that the proposed controller is effective.