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Error-bounds for balanced model-reduction of linear time-varying systems

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2 Author(s)
S. Lall ; Dept. of Aeronaut. & Astronaut., Stanford Univ., CA, USA ; C. Beck

Error-bounds are developed for balanced truncation of linear time-varying systems, leading to an extension of the "twice the sum of the tail" formulas, well known in the time-invariant case. The approach relies on an operator-theoretic framework for analysis of linear time-varying systems. This provides a multivariable notion of frequency for such systems, which are thus characterized by rational functions of many complex variables, allowing the problem to be formulated in the linear-fractional framework. Using a time-varying version of standard necessary conditions for reduced-order modeling, based on convex operator inequalities, we show that these error-bounds for balanced truncation are related to the closest possible reduced-order modeling error in a sense which parallels the time-invariant case.

Published in:

IEEE Transactions on Automatic Control  (Volume:48 ,  Issue: 6 )