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Simultaneous stabilization for a collection of nonlinear systems with uncertain parameter

Simultaneous stabilization for a collection of single-input nonlinear systems with uncertain parameter is dealt with in this paper. Necessary and sufficient conditions that a quadratic control Lyapunov function (CLF) is a common CLF for these systems are acquired. A systematic method to obtain quadratic CLFs by solving the Lyapunov equation is presented. A continuous state feedback control independently uncertain parameter is acquired. It can simultaneously stabilize these systems. Finally, the effectiveness of the proposed scheme is illustrated by a simulation example.