Saturated Controls for a PVTOL Aircraft and an Inertia Wheel Pendulum via a New Transformation

This paper presents saturation stabilization designs for a PVTOL aircraft and an inertia wheel pendulum employing a new transformation. With a coordinate transformation derived from the controllable matrix theory, the M-matrix theory allows us to directly determine the asymptotic stability of the reduced system that no longer contains saturation. Namely, without the need to construct Lyapunov functions, we can determine asymptotic stability by using row-diagonally dominant estimates. Also, the new treating method allows to provide a relatively optimal assignment of controller parameters in the sense that a relatively fast convergence can be guaranteed. Hopefully, the method in this paper may motivate new stabilizing designs for other complex physical systems.