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On the Global Analysis of Linear Systems

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Mathematical Control Theory

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Abstract

In this chapter, we present a number of topics in linear systems theory from a global, geometric perspective. Among the topics studied are the geometry of spaces of scalar and multivariable systems, the scalar and matrix valued Hermite-Hurwitz Theorem, and the geometry of the deterministic partial realization problem. Inverse eigenvalue problems are also formulated geometrically and studied in the context of both degree theory and intersection theory as computed in cohomology rings. Applications to the problem of pole assignment by output feedback are also reviewed, the paper concludes with a review of the recent solution to the rational covariance extension problem in both a geometric and a variational setting.

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  1. Christopher I. Byrnes
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Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, 02215-2407, USA

    J. Baillieul

  2. Mathematics Institute, University of Groningen, 9700 AV, Groningen, The Netherlands

    J. C. Willems

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Byrnes, C.I. (1999). On the Global Analysis of Linear Systems. In: Baillieul, J., Willems, J.C. (eds) Mathematical Control Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1416-8_4

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