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Controlled invariant subspace

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This is an old revision of this page, as edited by Jitse Niesen (talk | contribs) at 12:03, 27 November 2008 (looks like control theory for linear systems to me; some formatting, stub implies expand). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

A subspace V is called controlled invariant if for any x0 of V and an input u, is in V, for all nonnegative t.

Properties

Let V be a subspace of X. Then the following are equivalent:

  1. V is controlled invariant;
  2. AV is in V + Im B;
  3. There exist a feedback F such that (A + BF)V is in V.


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