An interpolated controller for stabilization of a plant with variable operating conditions

This paper considers stabilization of a linear time-invariant single-input/single-output plant with variable operating conditions. It is assumed that the plant is described by a linear interpolation of proper stable coprime factorizations of the transfer functions of two representative models which are defined at two representative operating points. A linear interpolation of stabilizing controllers for the representative models is applied to the interpolated plant. The necessary and sufficient condition for the interpolated plant to be stabilizable by the interpolated controller is presented using the Nevanlinna-Pick theory. It is also shown that simultaneous stabilizability of the two representative models is necessary for such stabilization. An example is given, which illustrates that the class of stabilizable plants via interpolated controllers is larger than that of plants stabilizable by fixed controllers.