Stabilization of a plant with time-varying operating conditions: an interpolated stabilizing controller

A stabilization problem is considered for a multi-input multi-output plant with time-varying operating conditions. The plant is described as an interpolation of two representative models defined at two representative operating points. To deal with the change of the plant dynamics, a state space description of an interpolated model, originally defined by coprime factorizations of transfer functions, is introduced. Corresponding to the plant description, a parameter-varying interpolated controller is defined as an interpolation of stabilizing controllers for the representative models. A BMI (bilinear matrix inequality) condition for the existence of such a stabilizing interpolated controller is presented. The condition is then reduced to LMIs (linear matrix inequalities) by restricting certain freedom in the choice of the interpolated controller