Robust stabilization of the 3DOF-helicopter using descriptor representation and polytope systems

In this paper, we show that the design method guarantees the robust stability the 3 dimensions of freedom helicopter. The dynamical equations of the helicopter are induced by Euler-Lagrange equation using the kinetic energy and the potential energy of the helicopter. These equations are not linear for the varying parameters. The Linear Fractional Transformation(LFT) and the descriptor representation are applied appropriately, and the state equations of polytopic form with regard to the varying parameters are given. The design problem is formulated by linear matrix inequalities(LMIs) to minimize the H∞ norm of the closed loop system. Then the stability of the system is guaranteed in the range of the parameter variation. The effectiveness of the proposed design method is illustrated by the simulations and the experiments.