Robust stabilization of discrete linear repetitive processes with switched dynamics

Jacek Bochniak; Krzysztof Galkowski; Eric Rogers; Anton Kummert

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 4, page 441-462
  • ISSN: 1641-876X

Abstract

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Repetitive processes constitute a distinct class of 2D systems, i.e., systems characterized by information propagation in two independent directions, which are interesting in both theory and applications. They cannot be controlled by a direct extension of the existing techniques from either standard (termed 1D here) or 2D systems theories. Here we give new results on the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.

How to cite

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Bochniak, Jacek, et al. "Robust stabilization of discrete linear repetitive processes with switched dynamics." International Journal of Applied Mathematics and Computer Science 16.4 (2006): 441-462. <http://eudml.org/doc/207805>.

@article{Bochniak2006,
abstract = {Repetitive processes constitute a distinct class of 2D systems, i.e., systems characterized by information propagation in two independent directions, which are interesting in both theory and applications. They cannot be controlled by a direct extension of the existing techniques from either standard (termed 1D here) or 2D systems theories. Here we give new results on the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.},
author = {Bochniak, Jacek, Galkowski, Krzysztof, Rogers, Eric, Kummert, Anton},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {uncertainty; repetitive processes; switched dynamics; stabilization; systems; 2D systems},
language = {eng},
number = {4},
pages = {441-462},
title = {Robust stabilization of discrete linear repetitive processes with switched dynamics},
url = {http://eudml.org/doc/207805},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Bochniak, Jacek
AU - Galkowski, Krzysztof
AU - Rogers, Eric
AU - Kummert, Anton
TI - Robust stabilization of discrete linear repetitive processes with switched dynamics
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 4
SP - 441
EP - 462
AB - Repetitive processes constitute a distinct class of 2D systems, i.e., systems characterized by information propagation in two independent directions, which are interesting in both theory and applications. They cannot be controlled by a direct extension of the existing techniques from either standard (termed 1D here) or 2D systems theories. Here we give new results on the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.
LA - eng
KW - uncertainty; repetitive processes; switched dynamics; stabilization; systems; 2D systems
UR - http://eudml.org/doc/207805
ER -

References

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  1. Amann N., Owens D.H. and Rogers E. (1998): Predictive optimal iterative learnig control. - Int. J. Contr., Vol. 69, No. 2, pp. 203-226. Zbl0949.93027
  2. Bachelier O., Bernussou J., de Oliveira M.C. and Geromel J.C.(1999): Parameter dependent Lyapunov control design: Numerical evaluation. - Proc. 38-th Conf. Decision and Control, Phoenix, USA, pp. 293-297. 
  3. Benton S.E. (2000): Analysis and Control of Linear Repetitive Processes. - Ph.D. thesis, University of Southampton, UK. 
  4. Bochniak J., Gałkowski K., Rogers E., Mehdi D., Bachelier O. and Kummert A. (2006): Stabilization of discrete linear repetitive processes with switched dynamics. - Multidim. Syst. Signal Process., Vol. 17, No. 2-3, pp. 271-293. Zbl1118.93037
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  6. D'Andrea R. and Dullerud G.E. (2003): Distributed control design for spatially interconnected systems. - IEEE Trans. Automat. Contr., Vol. 48, No. 9, pp. 1478-1495. 
  7. Du C. and Xie L. (1999): Stability analysis and stabilisation of uncertain two-dimensional discrete systems: An LMI approach. - IEEE Trans. Circ. Syst. I: Fundam. Theory Applic., Vol. 46, No. 11, pp. 1371-1374. Zbl0970.93037
  8. Edwards J.B. (1974): Stability problems in the control of multipass processes. - Proc. IEE, Vol. 121, No. 11, pp. 1425-1432. 
  9. Gałkowski K., Rogers E., Xu S., Lam J. and Owens D.H. (2002): LMIs-A fundamental tool in analysis and controller design for discrete linear repetitive processes. - IEEE Trans. Circ. Syst. I: Fundam. Theory Applic., Vol. 49, No. 6, pp. 768-778. 
  10. Longman R. (2003): On the interaction between theory, experiments and simulation in developing practical learning control algorithms. - Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 1, pp. 101-112. Zbl1046.93023
  11. Ratcliffe J.D., Hatonen J.J., Lewin P.L., Rogers E., Harte T.J. and Owens D.H. (2005): P-type iterative learning control for systems that contain resonance. - Int. J. Adapt. Contr. Sig. Process., Vol. 19, No. 10, pp. 769-796. Zbl1127.93365
  12. Roberts P.D. (2002): Two-dimensional analysis of an iterative nonlinear optimal control algorithm. - IEEE Trans. Circ. Syst. I: Fundam. Theory Applic., Vol. 49, No. 6, pp. 872-878. 
  13. Rogers E. and Owens D.H. (1992): Stability Analysis for Linear Repetitive Processes. -Lect. Notes Contr. Inf. Sci., Vol. 175, Berlin, Germany: Springer-Verlag. 
  14. Smyth K.J. (1992): Computer Aided Analysis for Linear Repetitive Processes. - Ph.D. thesis, University of Strathclyde, Glasgow, UK. 

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