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Balanced truncation of linear time-varying systems

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2 Author(s)
Sandberg, H. ; Dept. of Autom. Control, Lund Inst. of Technol., Sweden ; Rantzer, A.

In this paper, balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case of time-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.

Published in:

Automatic Control, IEEE Transactions on  (Volume:49 ,  Issue: 2 )