Simultaneous stabilization of a family of SISO nonlinear systems via output feedback

We cast the problem of robust stabilization of single-input single-output (SISO) nonlinear systems into a simultaneous stabilization problem. For a family of SISO affine in control nonlinear systems having a global normal form, we show that under certain conditions all the plants in this family is globally asymptotically stabilizable by a single parameterized linear output feedback control law. These conditions do not include the knowledge of relative degree of each plant of the family. We require only the knowledge of an upper bound on their relative degrees.