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sigma //0 is a real number. We construct a transfer function algebra of fractions, viz. F( sigma //0), for modeling possibly unstable distributed systems such that (i) f in F( sigma //0) is holomorphic in Re s greater than equivalent to sigma //0, (i. e. is sigma //0-stable) iff f is sigma //0-exponentially stable, and (ii) we allow delay in the direct input-output transmission of the system. This algebra is (a) a restriction of the algebra B( sigma //0) developed by Callier and Desoer, (b) an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained. The algebra F( sigma //0) can be used for modeling and feedback system design. It is shown that standard semigroup systems are better modeled by a transfer function in F( sigma //0) rather than B( sigma //0).
Original languageEnglish
Pages (from-to)1353-1373
Number of pages21
JournalInternational Journal of Control
Issue number5
Publication statusPublished - 1 May 1986

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