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Guaranteed error bounds for model reduction of linear time-varying systems

Techniques are presented for the model reduction of linear time-varying and linear periodically-varying systems, including the formulation and proof of guaranteed upper bounds for the error. The commonly used method of balanced truncation for linear time-invariant systems is generalized to the time-varying case with explicit error bounds that are derived based on generalizations of the 'twice-the-sum-of-the-tail' formula. The development of these reduction results for time-varying systems relies on a new operator framework for analysis of linear time-varying systems, presented in Dullerad and Lall (1997), in combination with the model reduction methods for uncertain systems developed in Beck et al. (1996).