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

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.

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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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