By Topic

Generalizations and new proof of the discrete-time positive real lemma and bounded real lemma

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Chengshan Xiao ; Wireless Networks, Nortel, Nepean, Ont., Canada ; Hill, D.J.

There are three different restatements claimed to be equivalent to the definition of discrete-time positive realness (DTPR) in the literature. These restatements were obtained by assuming that they are similar to the results of continuous-time positive realness when the transfer function has poles on the stability boundary. In this paper it is shown that only one of them is equivalent to the DTPR lemma and others are disproved by counter-examples. Furthermore, the DTPR lemma is specialized for minimal systems which have all poles on the unit cycle, the DTPR lemma is also generalized for nonminimal systems, the discrete-time bounded real (DTBR) lemma is proven by a simple method, and then the DTBR lemma is extended to the nonminimal case. Continuous-time results are also briefly considered in the Appendix

Published in:

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:46 ,  Issue: 6 )