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The orbit closure problem for matrix pencils: Necessary conditions and an application to high gain feedback. (English) Zbl 0736.93032
New trends in systems theory, Proc. Jt. Conf., Genoa/Italy 1990, Prog. Syst. Control Theory 7, 386-392 (1991).
Summary: [For the entire collection see Zbl 0726.00023.]
For a given state space system $$\Sigma$$, which singular systems can occur as a limit of $$\Sigma$$ under high gain feedback? We identify linear systems with rectangular matrix pencils and view this question in terms of orbit closure under the strict equivalence action of $$GL_ p\times GL_ q$$ on the space of $$p\times q$$ matrix pencils. We determine necessary conditions for a singular system to be a limit of a given state space system under high gain feedback.

##### MSC:
 93C15 Control/observation systems governed by ordinary differential equations 93C05 Linear systems in control theory