Novel Gramians for linear semistable systems

Xiaodong Cheng (Corresponding author), Jacquelien M.A. Scherpen

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo Gramians, and the controllability and observability energy functions are also characterized using the pseudo Gramians. Additionally, the H2-norm and H-norm of a semistable system are analyzed, and then the results are used for the model reduction of semistable systems. Finally, the effectiveness of the methods is illustrated by an example of a gene regulation network.

Original languageEnglish
Article number108911
Number of pages9
JournalAutomatica
Volume115
DOIs
Publication statusPublished - May 2020

Keywords

  • Controllability and observability
  • Gramian matrix
  • Linear system
  • Model reduction
  • Semistability

Fingerprint Dive into the research topics of 'Novel Gramians for linear semistable systems'. Together they form a unique fingerprint.

  • Cite this