Abstract
In Definition 4.3.5, we introduced the notion of a transfer function for a state linear system Σ(A, B, C. D) and showed that it was equal to D + C(sI – A)-1 B. In this section, we study the input-output relationship directly in the frequency domain without reference to any state-space descriptions. More specifically, we suppose that we have a scalar input function of time u: \(0,\infty ) \mapsto\) ℂ and a scalar output function of time y: \(0,\infty ) \mapsto \) ℂ, which arc Laplace transformable and we suppose that their Laplace transforms û(.) and ŷ(.) are related by
where g(s) is an irrational function of the complex variable s. We call the g(s) the transfer function.
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© 1995 Springer-Verlag New York, Inc.
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Curtain, R.F., Zwart, H. (1995). Frequency-Domain Descriptions. In: An Introduction to Infinite-Dimensional Linear Systems Theory. Texts in Applied Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4224-6_7
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DOI: https://doi.org/10.1007/978-1-4612-4224-6_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8702-5
Online ISBN: 978-1-4612-4224-6
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