✦ LIBER ✦

Quadratic stability in the circle theorem or positivity theorem

✍ Scribed by Duksun Shim

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 415 KB
Volume: 6
Category: Article
ISSN: 1049-8923
DOI: 10.1002/(sici)1099-1239(199610)6:8<781::aid-rnc189>3.0.co;2-k

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✦ Synopsis

In this technical note, we study the quadratic stability problem for linear time-invariant multi-input, multioutput systems which have time-varying sector-bounded or positive real uncertainty feedback. It is known that the circle theorem and positivity theorem are sufficient conditions for robust stability, for sectorbounded and positive real feedback, respectively. We show that the circle theorem is necessary and sufficient condition for quadratic stability when the feedback is sector-bounded, and that the positivity theorem is necessary and sufficient condition for quadratic stability when the feedback is positive-real.

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