On the Global Analysis of Linear Systems

  • Christopher I. Byrnes


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.


Output Feedback Maslov Index Hankel Matrix Pole Assignment Linear System Theory 
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