Guaranteed Error Bounds for Model Reduction of Linear Time-Varying Systems

New 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 [G. Dullerud and S. Lall. A new approach for analysis and synthesis of time-varying systems. Proceedings of the IEEE Conference on decision and control, 1997], in combination with the model reduction methods for uncertain systems developed in [C. L. Beck, J. C. Doyle, and K. Glover. Model reduction of multidimensional and uncertain systems. IEEE Transactions on Automatic Control, 41:1466--1477, October 1996.]