Time Variant Balancing and Nonlinear Balanced Realizations

Balancing for linear time varying systems and its application to model reduction via projection of dynamics (POD) are briefly reviewed. We argue that a generalization for balancing nonlinear systems may be expected to be based upon three sound principles: 1) Balancing should be defined with respect to a nominal flow; 2) Only Gramians defined over small time intervals should be used in order to preserve the accuracy of the linear perturbation model and; 3) Linearization should commute with balancing, in the sense that the linearization of a globally balanced model should correspond to the balanced linearized model in the original coordinates.

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