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Bilinear control of Toeplitz formations
Author(s) -
Rüppel 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.201100164
Subject(s) - toeplitz matrix , mathematics , invertible matrix , circulant matrix , pure mathematics , bilinear form , algebra over a field , unitary matrix , matrix (chemical analysis) , unitary state , bilinear interpolation , product (mathematics) , matrix analysis , discrete mathematics , eigenvalues and eigenvectors , physics , quantum mechanics , statistics , materials science , geometry , political science , law , composite material
We investigate controllability properties of bilinear control systems, defined by classes of Toeplitz matrices. It is shown that the Lie algebra of all pseudo‐circulant matrices coincides with the full matrix Lie algebra. This implies the controllability of associated bilinear control systems. As a by‐product we deduce that every complex invertible matrix is the finite product of invertible Toeplitz matrices; moreover, every complex unitary matrix is shown to be a finite product of complex unitary Toeplitz matrices.