A Fractional Approach to Model Reduction

A new method for the model reduction of finite-dimensional, linear, time-invariant (FDLTI) plants is given. The method uses fractional representation theory to extend balance and trancate model reduction to unstable plants without requiring the ad-hoc division of the plant into stable and completely unstable parts. The new method, dubbed fractional balanced reduction or FBR, applies balance and truncate to a special representation of the graph operator of the plant. This operation yields an object readily recognized as the graph operator of a reduced order plant. The method has nice properties including existence of an a priori error bound in the graph metric, and preservation of sector containment which is useful for deciding system stability when nonlinearities are present.