Characterization of Sign Controllability for Linear Systems with Real Eigenvalues.

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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Abstract:
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:

@InProceedings{HartungReissigSvaricek13c,
  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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