Error bounds for balanced truncation of linear time-varying systems

Author

Sandberg, Henrik ; Rantzer, Anders

Author_Institution

Lund Inst. of Technol., Sweden

Volume

3

fYear

2002

fDate

10-13 Dec. 2002

Firstpage

2892

Abstract

In this paper error bounds for truncated balanced linear time-varying systems in discrete time are obtained. The analysis is based on direct calculations with the time-varying observability and controllability Lyapunov inequalities. The obtained bounds in the induced ₂-norm, generalize well-known error-bound formulas for time-invariant systems. The case of time-varying state-space dimension is considered, and this proves to be valuable both for technical and practical reasons. The input-output stability of truncated models is shown to be guaranteed.

Keywords

Lyapunov methods; controllability; discrete time systems; linear systems; observability; reduced order systems; stability; state-space methods; time-varying systems; Lyapunov inequalities; balanced truncation; controllability; discrete time systems; error bounds; line systems; model reduction; observability; state-space dimension; time-varying systems; Automatic control; Chemicals; Error correction; Linear systems; Nonlinear systems; Observability; Reduced order systems; Stability; Switches; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2002, Proceedings of the 41st IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7516-5

Type

conf

DOI

10.1109/CDC.2002.1184288

Filename

1184288