154
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Equivalent 2-D nonsingular Roesser models for discrete linear repetitive processes

, &
Pages 2673-2681 | Received 14 Nov 2016, Accepted 28 Nov 2017, Published online: 26 Dec 2017

References

  • Attasi, S. (1973). Systemes lineaires homogenes a deux indices ( Rapport Laboria No. 31). Rocquencourt, France: IRIA.
  • Boudellioua, M. , Galkowski, K. , & Rogers, E. (2017). On the connection between discrete linear repetitive processes and 2-D discrete linear systems. Multidimensional Systems and Signal processing, 28 , 341–351.
  • Cichy, B. , Galkowski, K. , Rogers, E. , & Kummert, A. (2013). Control law design for discrete linear repetitive processes with non-local updating structures. Multidimensional Systems and Signal Processing, 24 , 707–726.
  • Fornasini, E. , & Marchesini, G. (1976). State space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control, AC-21 , 484–492.
  • Galkowski, K . (2001). State space realization of linear 2-D systems with extensions to the general nD (n > 2) case . London: Springer.
  • Galkowski, K. , Rogers, E. , & Owens, D. H. (1998). Matrix rank based tests for reachabiltiy/controllability of discrete linear repetitive processes. Linear Algebra and its Applications, 275–276 , 201–224.
  • Galkowski, K. , Rogers, E. , & Owens, D. H. (1999). New 2D models and a transition matrix for discrete linear repetitive processes. International Journal of Control, 72 , 1365–1380.
  • Hladowski, L. , Galkowski, K. , Cai, Z. , Rogers, E. , Freeman, C. T. , & Lewin, P. (2010). Experimentally supported 2D systems based iterative learning control law design for error convergence and performance. Control Engineering Practice, 18 , 339–348.
  • Hladowski, L. , Galkowski, K. , Cai, Z. , Rogers, E. , Freeman, C. T. , & Lewin, P. L. (2012). Output information based iterative learning control law design with experimental verification. ASME Journal of Dynamic Systems, Measurement and Control, 134 , 021012/1–021012/10.
  • Johnson, D . (1993). Coprimeness in multidimensional system theory and symbolic computation . Ph.D thesis. UK: Loughborough University of Technology.
  • Johnson, D. , Pugh, A. , Rogers, E. , Hayton, G. , & Owens, D. H. (1996). A polynomial matrix theory for a certain class of two-dimensional linear systems. Linear Algebra and its Applications, 241–243 , 669–703.
  • Levy, B . (1981). 2-D polynomial and rational matrices and their applications for the modelling of 2-D dynamical systems . Ph.D thesis. USA: Stanford University.
  • Paszke, W. , Rogers, E. , & Galkowski, K. (2016). Experimentally verified generalized KYP lemma based iterative learning control design. Control Engineering Practice, 53 , 57–67.
  • Pugh, A. , McInerney, S. , Boudellioua, M. , Johnson, D. , & Hayton, G. (1998). A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock. International Journal Control, 71 , 491–503.
  • Pugh, A. , McInerney, S. , Hou, M. , & Hayton, G . (1996). A transformation for 2-D systems and its invariants. In Proceedings of the 35th IEEE conference on decision and control (pp. 2157–2158). Kobe, Japan: IEEE Control Systems Society.
  • Roesser, R. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic, AC-20 , 1–10.
  • Rogers, E. , Galkowski, K. , & Owens, D. H . (2007). Control systems theory and applications for linear repetitive processes, control and information sciences . Berlin Heidelberg: Springer-Verlag.
  • Rosenbrock, H. H . (1970). State space and multivariable theory . London: Nelson-Wiley.
  • Xu, L. , Yan, S. , Lin, Z. , & Matsushita, S. (2012). A new elementary operation approach to multidimensional realization and LFR uncertainty modeling: The MIMO case. IEEE Transactions on Circuits and Systems-I, 59 , 638–651.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.