Transfer functions of infinite-dimensional systems: positive realness, stabilization and absolute stability

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• Chris Guiver, University of Bath
• Friday 24 February 2017, 14:00-15:00
• Cambridge University Engineering Department, LR3A.

If you have a question about this talk, please contact Tim Hughes.

I shall present recent work with others on a general class of operator-valued irrational positive-real functions with an emphasis on their frequency-domain properties and the relation with stabilization by output feedback. Such functions arise naturally as the transfer functions of numerous infinite-dimensional control systems, including examples specified by PDEs. Our results include characterizations of positive realness in terms of imaginary axis conditions, as well as characterizations in terms of stabilizing output feedback, where both static and dynamic output feedback is considered. One motivation for the present study is to prepare the way for absolute and input-to-state stability results for Lur’e systems in an infinite dimensional setting. Positive realness provides a viable approach to proving stability in this context and arises in conditions such as the well-known circle criterion which shall be discussed.

This talk is part of the CUED Control Group Seminars series.

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