Abstract
In Chapters 6 through 10 we saw how the distance formulas and factorization theorems described in Chapter 3 provided an elegant framework for the formulation and solution of problems relating to stabilization and robustness of linear time-varying systems. Here we consider a problem that has its origins in classical network theory. A network is characterized as a stable linear systems as defined in Section 5.5.Sis passive ifI — S*S≥ 0, and lossless ifI — S*S= 0. In operator theoretic terminology, passive systems are contractions, ‖S‖ ≤ 1, and lossless systems are isometries.
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References, Notes, and Remarks
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Feintuch, A. (1998). Orthogonal Embedding of Time-Varying Systems. In: Robust Control Theory in Hilbert Space. Applied Mathematical Sciences, vol 130. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0591-3_11
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DOI: https://doi.org/10.1007/978-1-4612-0591-3_11
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