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Hankel norm approximation for infinite-dimensional systems. (English) Zbl 1009.93501

Lecture Notes in Control and Information Sciences. 277. Berlin: Springer. viii, 144 p. (2002).
This monograph presents results of the thesis of the author obtained at the University of Groningen. The general theme is the approximation of infinite-dimensional linear systems by finite-dimensional ones. This model reduction problem is handled with the use of the Hankel norm. After a descriptive chapter on well-posed linear systems including the Pritchard-Salomon class and the exponentially stable analytic systems, the author studies the nuclearity and the compactness of the Hankel operator, which is used later. Chapter four is a frequency domain characterization of the suboptimal Hankel norm approximation problem through the solution of a J-spectral approximation problem. Here one makes certain assumptions on the transfer function. In the next chapter it is seen that these assumptions are satisfied for the smooth Pritchard-Salomon class of exponentially stable systems with finite-dimensional input and output spaces (FDIOS). Similar kinds of results are obtained for the analytic class of exponentially stable systems with FDIOS. The J-spectral factors are expressed in terms of state-space parameters in both cases. The rest of the book explores generalizations (relaxation of the exponential stability assumption, regular systems). A bibliography (94 entries), an index and notations are found at the end.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B11 System structure simplification
93B28 Operator-theoretic methods
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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