Gunther Reissig,
Christoph Hartung,
and Ferdinand Svaricek.

Strong Structural Controllability and Observability of Linear Time-Varying Systems.

IEEE Trans. Automat. Control, vol. 59, no. 11, Nov. 2014, pp. 3087-3092.

Full text.
(Definitive publication; restricted access.)

Full text.
(Accepted version; free access.)

**Abstract:**

In this note we consider continuous-time systems
$x\text{'}(t)\; =\; A(t)\; x(t)\; +\; B(t)\; u(t)$,
$y(t)\; =\; C(t)\; x(t)\; +\; D(t)\; u(t)$
as well as discrete-time systems
$x(t+1)\; =\; A(t)\; x(t)\; +\; B(t)\; u(t)$
$y(t)\; =\; C(t)\; x(t)\; +\; D(t)\; u(t)$
whose coefficient matrices
$A$,
$B$,
$C$ and
$D$
are not exactly known. More precisely, all that is known about the
systems is their nonzero pattern, i.e., the locations of the nonzero
entries in the coefficient matrices. We characterize the patterns that
guarantee controllability and observability, respectively, for all
choices of nonzero time functions at the matrix positions defined by
the pattern, which extends a result by Mayeda and Yamada for
time-invariant systems. As it turns out, the conditions on the
patterns for time-invariant and for time-varying discrete-time systems
coincide, provided that the underlying time interval is sufficiently
long. In contrast, the conditions for time-varying continuous-time
systems are more restrictive than in the time-invariant case.

**BibTeX entry:**

@InProceedings{ReissigHartungSvaricek14,
author = {Gunther Reissig and Christoph Hartung and Ferdinand Svaricek},
title = {Strong Structural Controllability and Observability of Linear Time-Varying Systems},
year = 2014,
journal = {IEEE Trans. Automat. Control},
volume = 59,
number = 11,
pages = {3087-3092},
month = nov,
doi = {10.1109/TAC.2014.2320297}
}

Impressum und Haftungsausschluß