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.

Full text.
(Definitive publication; restricted access.)

Full text.
(Free access.)

**Abstract:**

A linear time-invariant system of the form
$x\text{'}(t)\; =\; A\; x(t)\; +\; B\; u(t)$,
or
$x(t\; +\; 1)\; =\; A\; x(t)\; +\; B\; u(t)$
is sign controllable if all linear time-invariant systems whose
matrices $A\text{'}$
and $B\text{'}$ 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}
}

Impressum und Haftungsausschluß