Representation of Feedback Operators for Hyperbolic Systems
نویسندگان
چکیده
We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numerical results are given to illustrate the role that damping plays in the smoothness of these gains. *This research was supported in part by the Air Force Office of Scientific Research under grant F49620-93-1-0280 and by the National Aeronautics and Space Administration under contract No. NASA-19480 while the author was a visiting scientist at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681-0001. tThls research was supported in part by the Air Force Office of Scientific Research under grant F49620-93-1-0280 while the author was a visiting scientist at the Air Force Center for Optimal Design and Control, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0531, and by the National Science Foundation under grant DMS-9409506.
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