Balanced truncation for unstable infinite dimensional systems via reciprocal transformation

We discuss a model reduction for unstable infinite dimensional systems using balanced truncation of reciprocal systems. The systems considered are assumed to be exponentially stabilizable and detectable, with bounded and finite rank input and output operators. We decompose the systems into their sta...

Full description

Saved in:
Bibliographic Details
Published in:International journal of control, automation, and systems 2011, Automation, and Systems, 9(2), , pp.249-257
Main Authors: Fatmawati, Saragih, Roberd, Bambang, Riyanto T., Soeharyadi, Yudi
Format: Article
Language:English
Subjects:
Approximation
Balancing
Computer simulation
Control
Control systems
Decomposition
Engineering
Heat equations
Hilbert space
Mathematical analysis
Mathematical models
Mathematics
Mechatronics
Partial differential equations
Reduction
Regular Papers
Robotics
Transformations
제어계측공학
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss a model reduction for unstable infinite dimensional systems using balanced truncation of reciprocal systems. The systems considered are assumed to be exponentially stabilizable and detectable, with bounded and finite rank input and output operators. We decompose the systems into their stable and unstable parts and perform reciprocal transformation only on the stable part. Balanced truncation is carried out on the reciprocal systems. This yield is then translated using reciprocal transformation as the reduced-order model of the stable part. Finally, we added the unstable part to the reduction of the stable part as the overall reduced-order model for the systems. To verify the effectiveness of the proposed approach, numerical simulations are applied to the heat equation. The performance of the proposed reduction method is compared to the balanced truncation method.
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-011-0206-3