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In this paper we establish a Lebeau-Robbiano spectral inequality for adegenerated one dimensional elliptic operator and show how it can be used toimpulse control and finite time stabilization for a degenerated parabolicequation. R{\'e}sum{\'e} .-Dans cet article, on s'int{\'e}r{\`e}ss{\`e} al'in{\'e}galit{\'e} spectrale de type Lebeau-Robbiano sur la somme de fonctionspropres pour une famille d'op{\'e}rateurs d{\'e}g{\'e}n{\'e}r{\'e}s. Lesapplications sont donn{\'e}es en th{\'e}orie du contr{\^o}le comme lecontr{\^o}le impulsionnel et la stabilisation en temps fini.

A spectral inequality for degenerated operators and applications