Christoph Hartung, Gunther Reissig, and Ferdinand Svaricek.
Characterization of Sign Controllability for Linear Systems with Real Eigenvalues.
Proc. Australian Control Conference (AUCC), Perth, Australia, 4-5 Nov. 2013, pp. 450-455.
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A linear time-invariant system of the form x'(t) = A x(t) + B u(t), or x(t + 1) = A x(t) + B u(t) is sign controllable if all linear time-invariant systems whose matrices A' and B' have the same sign pattern as A and B are controllable. This work characterizes the sign controllability for systems, whose sign pattern of A allows only real eigenvalues. Moreover, we present a combinatorial condition which is necessary for sign controllability and we show that if this condition is satisfied, then in all linear time-invariant systems with that sign pattern, all real eigenvalues of A are controllable. In addition, it is proven that the decision whether a linear time-invariant systems is not sign controllable is NP-complete. We want to emphasize, that our results cover the single and the multi-input case.
BibTeX entry:
  author = {Christoph Hartung and Gunther Reissig and Ferdinand Svaricek},
  title  = {Characterization of Sign Controllability for Linear Systems with Real Eigenvalues},
  booktitle = {Proc. Australian Control Conf. (AUCC), Perth, Australia, 4-5 } # nov # { 2013},
  PAGES  = {450-455},
  YEAR  = 2013,
  doi = {10.1109/AUCC.2013.6697315}

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