A unified view of Balanced Truncation and Singular Perturbation Approximations

Abstract

This paper demonstrates that both Balanced Truncation and Balanced Singular Perturbation Approximations can be viewed as limiting approximations of the same parameterization of Linear Time Invariant (LTI) systems. First, we introduce a specific parameterization of LTI systems that distinguishes dynamic and structural parameters. Next, we apply the Model Boundary Approximation Method (MBAM) [1] to particular parameters to achieve different approximations. This unified view of these popular model reduction techniques, which themselves can result in quite different approximations, illustrates that each approximation corresponds to a particular boundary element on a manifold, the “model manifold,” which is associated with the specific choice of model parameterization and is embedded in a sample space of measured outputs.