Abstract
Crossed product algebras are proposed as a framework for the study of input-output properties of linear time-varying systems. It is shown that internally stable systems with bounded continuous coefficients have transfer operators in a crossed product and conversely, that the set of all such transfer operators is dense in a crossed product. It is also shown that crossed product algebras admit causal additive decompositions, and allow a generalized frequency-domain representation.
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Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR 80-156. The United States Government is authorized to produce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
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Murray, J. Time-varying systems and crossed products. Math. Systems Theory 17, 217–241 (1984). https://doi.org/10.1007/BF01744442
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DOI: https://doi.org/10.1007/BF01744442