Christoph Hartung,
Gunther Reißig,
and Ferdinand Svaricek.

Characterization of Strong Structural Controllability of Uncertain Linear Time-Varying Discrete-Time Systems.

Proc. 51th IEEE Conf. Decision and Control (CDC), Maui, Hawaii,
U.S.A., 10-13 Dec. 2012, pp. 2189-2194.

Full text.
(Definitive publication; restricted access.)

**Abstract:**

We extend earlier characterizations of strong structural
controllability of linear systems depending on parameters to the
time-varying case
$x(t+1)\; =\; A$_{t} x(t) + B_{t} u(t).
Our main result is that the time-varying system is strongly
structurally controllable iff the corresponding time-invariant system
(whose matrices have the same zero-nonzero structure) is so. We also
establish that every strongly structurally controllable time-varying
system is controllable on every time interval of the form
$\{t,t+1,...,t+n\}$, where
$n$ is the dimension of the state space, a
property which is not, in general, valid for linear
time-varying systems that are merely controllable. Finally, we present
an algorithm for verifying the property of strong structural
controllability. Our results cover the single- and multi-input cases and
apply without any assumptions on the systems' structure or the
time-varying entries of $A$ and $B$.

**BibTeX entry:**

@InProceedings{HartungReissigSvaricek12,
author = {Christoph Hartung and Gunther Rei{\ss}ig and Ferdinand Svaricek},
title = {Characterization of Strong Structural Controllability of Uncertain Linear Time-Varying Discrete-Time Systems},
booktitle= {Proc. 51st IEEE Conf. Decision and Control (CDC), Maui, Hawaii, U.S.A., 10-13 } # dec # { 2012},
PAGES = {2189-2194},
YEAR = 2012,
PUBLISHER= {IEEE},
doi = {10.1109/CDC.2012.6426326}
}

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