NDLI: Strong stabilization of almost passive linear systems

Content Provider	IEEE Xplore Digital Library
Author	Weiss, G. Curtain, R.F.
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Electron. Eng., Imperial Coll. London (Weiss, G.)
Abstract	The plant to be stabilized is a system node Sigma with generating triple (A, B, C) and transfer function G, where A generates a contraction semigroup on the Hilbert space X. The control and observation operators B and C may be unbounded and they are not assumed to be admissible. The crucial assumption is that there exists a bounded operator E such that, if we replace G(s) by G(s) + E, the new system $Sigma_{E}$ becomes impedance passive. A trivial case is when G is already impedance passive and a special case is when Sigma has colocated sensors and actuators. Such systems include many wave, beam and heat equations with sensors and actuators on the boundary. It has been shown for many particular cases that the feedback u = -ky + v, where u is the input of the plant and k > 0, stabilizes Sigma, strongly or even exponentially. Here, y is the output of Sigma and v is the new input. Our main result is that if for some E isin L(U), $Sigma_{E}$ is impedance passive, and Sigma is approximately observable or approximately controllable in infinite time, then for sufficiently small k the closed-loop system is weakly stable. If, moreover, sigma(A)capiRopf is countable, then the closed-loop semigroup and its dual are both strongly stable. We illustrate our results with three classes of second order systems, only one of which has colocated actuators and sensors
Starting Page	4688
Ending Page	4693
File Size	192385
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377191
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear systems Impedance Actuators Control systems Sensor systems Transfer functions Hilbert space Equations Thermal sensors Feedback
Content Type	Text
Resource Type	Article

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