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Stabilization for a collection of feedback linearizable systems

Stabilization for a collection of feedback linearizable systems with uncertain parameter is dealt with in this paper. Necessary and sufficient conditions for a quadratic control Lyapunov function to be a common control Lyapunov function for these systems are obtained. A continuous state feedback control is designed based on the common control Lyapunov function. It can simultaneously stabilize these systems. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example.