Controllability and observability of time-invariant linear dynamic systems

Martin Bohner; Nick Wintz

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 2, page 149-163
  • ISSN: 0862-7959

Abstract

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In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.

How to cite

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Bohner, Martin, and Wintz, Nick. "Controllability and observability of time-invariant linear dynamic systems." Mathematica Bohemica 137.2 (2012): 149-163. <http://eudml.org/doc/246984>.

@article{Bohner2012,
abstract = {In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.},
author = {Bohner, Martin, Wintz, Nick},
journal = {Mathematica Bohemica},
keywords = {time scale; dynamic equation; exponential function; controllability; reachability; observability; duality principle; time invariance; time scale; dynamic equation; controllability; reachability; observability; duality principle},
language = {eng},
number = {2},
pages = {149-163},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Controllability and observability of time-invariant linear dynamic systems},
url = {http://eudml.org/doc/246984},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Bohner, Martin
AU - Wintz, Nick
TI - Controllability and observability of time-invariant linear dynamic systems
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 2
SP - 149
EP - 163
AB - In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.
LA - eng
KW - time scale; dynamic equation; exponential function; controllability; reachability; observability; duality principle; time invariance; time scale; dynamic equation; controllability; reachability; observability; duality principle
UR - http://eudml.org/doc/246984
ER -

References

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  2. Bartosiewicz, Z., Pawłuszewicz, E., Linear control systems on time scales: unification of continuous and discrete, Proc. of 10th IEEE Int. Conference MMAR. (2004), 263-266. (2004) MR2323260
  3. Bartosiewicz, Z., Pawłuszewicz, E., Realizations of linear control systems on time scales, Control Cybernet. 35 (2006), 769-786. (2006) Zbl1133.93033MR2323260
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  7. Davis, J. M., Gravagne, I. A., Jackson, B. J., II, R. J. Marks, Controllability, observability, realizability, and stability of dynamic linear systems, Electron. J. Diff. Equ. 37 (2009), 1-32. (2009) MR2495842
  8. Fausett, L. V., Murty, K. N., Controllability, observability and realizability criteria on time scale dynamical systems, Nonlinear Stud. 11 (2004), 627-638. (2004) MR2100755
  9. Hilscher, R., Zeidan, V., Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Anal. 70 (2009), 3209-3226. (2009) Zbl1157.49030MR2503067
  10. Kalman, R. E., Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana. 2 (1960), 102-119. (1960) Zbl0112.06303MR0127472
  11. Kalman, R. E., On the general theory of control systems, Proc. 1st IFAC Congress Automatic Control. 1 (1960), 481-492. (1960) 
  12. Kalman, R. E., Mathematical description of linear dynamical systems, J. SIAM Control Ser. A Control. 1 (1963), 152-192. (1963) Zbl0145.34301MR0152167
  13. Kalman, R. E., Ho, Y. C., Narendra, K. S., Controllability of linear dynamical systems, Contrib. Differ. Equ. 1 (1963), 189-213. (1963) Zbl0151.13303MR0155070
  14. Molnar, S., Szigeti, F., Controllability and reachability of dynamic discrete-time linear systems, Proceedings of the 4th International Conference on Control and Automation (2003), 350-354. (2003) MR1368381
  15. Wintz, N., The Kalman filter on time scales, PhD Thesis, Missouri University of Science and Technology, Rolla, Missouri, USA (2009). (2009) MR2941934
  16. Zafer, A., 10.1017/S1446181100003436, ANZIAM J. 48 (2006), 99-106. (2006) MR2263186DOI10.1017/S1446181100003436

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