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In this paper, new sufficient Lyapunov-like stability conditions and new Lyapunov-like, stabilizability conditions for nonlinear descriptor systems, with control, are presented along with their applications to quadcopter's flight stabilization. Most of these results are rather practical because they do not need solving nonlinear differential equations and nonlinear algebraic equations. Thus, the usage of these new results requires only the differentiation of functions. The numerical simulation results prove that the stabilization of the quadcopter is improved, in comparison with pure tracking control.

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