Fractional balanced reduction: model reduction via fractional representation

A method for the model reduction of finite-dimensional, linear, time-invariant (FDLTI) plants is proposed which uses normalized fractional representations is proposed. The method, dubbed fractional balanced reduction, applies balance and truncate to a special representation of the graph operator of the plant. This operation yields the graph operator of a reduced order plant. The method has such properties as existence of an a priori error bound in the graph metric and preservation of sector containment. Coupling fractional representations with principal component analysis gives a model reduction method that is capable of producing, in a numerically stable way, a good reduced order model using the whole full order model. Sector properties are also preserved-these are useful for deciding stability when nonlinearities are in the loop