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Entropy of controlled invariant subspaces
Author(s) -
Colonius F.,
Helmke U.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100105
Subject(s) - linear subspace , mathematics , subspace topology , eigenvalues and eigenvectors , invariant subspace , invariant (physics) , entropy (arrow of time) , upper and lower bounds , pure mathematics , mathematical analysis , physics , mathematical physics , quantum mechanics
For continuous‐time linear control systems invariance entropy of controlled invariant subspaces is introduced. It is shown that it coincides with a variant of topological entropy for linear flows which we call subspace entropy. Using this characterization, upper bounds in terms of eigenvalues of an induced flow are derived. Under additional assumptions (diagonalizability, single inputs) these bounds are improved.