Mathematical Sciences: Systems Theory, Transfer Functions and Geometry

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The principal investigator proposes to address the problem of pole placement by dynamic compensation for time-invariant linear control systems. One goal is to find sufficient and almost necessary conditions for the pole placemnt map with real dynamic compensators tobe onto, giving exact bounds for the minimal order real compensator. Another is to study various topological questions related to the space of multivariable linear systems with a fixed McMillan degree leading to a comparative analysis of physically natural compactifications. The pole placement problem is fundamental in linear systems theory. Linear systems remain important in many applied situations.