Balanced truncation of linear time-varying systems

Author

Sandberg, Henrik ; Rantzer, Anders

Author_Institution

Dept. of Autom. Control, Lund Inst. of Technol., Sweden

Volume

49

Issue

2

fYear

2004

Firstpage

217

Lastpage

229

Abstract

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.

Keywords

Lyapunov matrix equations; continuous time systems; discrete time systems; input-output stability; invariance; linear systems; observability; reachability analysis; reduced order systems; time-varying systems; Lyapunov equations; Lyapunov inequalities; balanced truncation; continuous time; discrete time; error bound; high-order model; input-output stability; linear time-varying systems; model reduction; observability; reachability; state-dimension; time-invariant formulas; Asymptotic stability; Councils; Linear approximation; Linear systems; Nonlinear systems; Reduced order systems; Riccati equations; Robust control; Sufficient conditions; Time varying systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2003.822862

Filename

1266776