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Using an observer to transform linear systems into strictly positive real systems

Collado, J.; Lozano, R. and Johansson, Rolf LU (2007) In IEEE Transactions on Automatic Control 52(6). p.1082-1088
Abstract
In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
strictly positive realness (SPR), passivity, observers, Kalman-Yakubovich-Popov (KYP) lemma, Lyapunov functions, strictly positive realness, (SPR) systems
in
IEEE Transactions on Automatic Control
volume
52
issue
6
pages
1082 - 1088
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000247353300013
  • scopus:34447128726
ISSN
0018-9286
DOI
10.1109/TAC.2007.899074
language
English
LU publication?
yes
id
da9fd32b-007b-4e76-80e6-de0bfc828f8e (old id 648449)
date added to LUP
2007-12-10 11:44:06
date last changed
2017-05-21 04:16:39
@article{da9fd32b-007b-4e76-80e6-de0bfc828f8e,
  abstract     = {In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples.},
  author       = {Collado, J. and Lozano, R. and Johansson, Rolf},
  issn         = {0018-9286},
  keyword      = {strictly positive realness (SPR),passivity,observers,Kalman-Yakubovich-Popov (KYP) lemma,Lyapunov functions,strictly positive realness,(SPR) systems},
  language     = {eng},
  number       = {6},
  pages        = {1082--1088},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Using an observer to transform linear systems into strictly positive real systems},
  url          = {http://dx.doi.org/10.1109/TAC.2007.899074},
  volume       = {52},
  year         = {2007},
}