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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.

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