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On generic properties of linear systems: An overview. (English) Zbl 0546.93020

Summary: The topological space of linear, time-invariant systems is considered. A property of linear systems is called generic if the systems equipped with this property occupy an open and dense subspace of the space of systems. Several generic properties of linear systems are reviewed, including controllability, invertibility, structural stability, as well as some topological properties of orbits of the feedback group. A new estimate for the number of orbits of the feedback group is produced, and a differential geometric proof of the existence of generic controllability indices is given.

MSC:

93B25 Algebraic methods
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93B05 Controllability
93B07 Observability
93D15 Stabilization of systems by feedback
93C99 Model systems in control theory
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References:

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