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Stabilization of the Inertia Wheel Pendulum by Time-Delayed State Feedback

Through coordinate changes and an initial control design, the inertia wheel pendulum is transformed into a feedforward-type system with higher order nonlinear terms, and then a controller is suggested to attenuate the higher order terms. Partial state variables in the controller admit moderate small saturation restriction and time delay. The global asymptotic stability of the closed-loop system is proven by showing that it has no finite escape time and converges to an asymptotically stable dynamics in finite time. Simulation results show that the proposed design is effective.