An interpolated controller for a plant with variable operating conditions

This paper considers stabilization of linear time-invariant single-input single-output plants with variable operating conditions. The plant is assumed to be described by a linear interpolation of nominal models which are defined at two representative operating points and written in proper stable factorizations of their transfer functions. A linear interpolation of controllers stabilizing the nominal models is applied to the interpolated plant. The necessary and sufficient condition for stabilizability is obtained using the Nevanlinna-Pick interpolation theory. The class of stabilizable plants via interpolated controllers is larger than that of plants stabilizable by fixed controllers. The relation to the simultaneous stabilization problem for nominal models is also considered