In this brief, stabilization designs are presented for a planar vertical takeoff and landing (PVTOL) aircraft and an inertia wheel pendulum (IWP). In the design procedure, the IWP and a subsystem of the PVTOL aircraft are transformed into chains of integrators with nonlinear perturbations, and then a saturated control technique is employed. The closed-loop systems are shown to be globally asymptotically stable via simple Lyapunov analysis. With the aid of the saturation technique, the designs require neither backstepping/forwarding techniques nor small gain analysis, and their effectiveness is demonstrated by numerical simulations.
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Ye et al. (2007) studied this question.
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