On exponential stability of a class of descriptor continuous linear 2D Roesser models

References

• Agathoklis, P., Jury, E. I., & Mansour, M. (1991). Algebraic necessary and sufficient conditions for the very strict hurwitz property of a 2-D polynomial. Multidimensional Systems and Signal Processing, 2(1), 45–53. https://doi.org/10.1007/BF01940471
   Web of Science ®Google Scholar
• Augusta, P., & Hurak, Z. (2013). Distributed stabilisation of spatially invariant systems: positive polynomial approach. Multidimensional Systems and Signal Processing, 24(1), 3–21. https://doi.org/10.1007/s11045-011-0152-5
   Web of Science ®Google Scholar
• Bachelier, O., Cluzeau, T., Silva Alvarez, F. J., & Yeganefar, N. (2020). Stability of one-dimensioned spatially interconnected systems. Multidimensional Systems and Signal Processing, 31(3), 1005–1028. https://doi.org/10.1007/s11045-019-00695-y
   Web of Science ®Google Scholar
• Bachelier, O., Paszke, W., Yeganefar, N., & Mehdi, D. (2018). Comments on ‘On stabilization of 2D Roesser models’. IEEE Transactions on Automatic Control, 63(8), 2745–2749. https://doi.org/10.1109/TAC.2017.2767282
   Web of Science ®Google Scholar
• Bachelier, O., Paszke, W., Yeganefar, N., Mehdi, D., & Cherifi, A. (2014). Towards LMI necessary and sufficient stability conditions for 2D Roesser models (Research Report), available upon request at http://www.lias-lab.fr/perso/olivierbachelier/.
   Google Scholar
• Bachelier, O., Paszke, W., Yeganefar, N., Mehdi, D., & Cherifi, A. (2016). LMI stability conditions for 2D roesser models. IEEE Transactions on Automatic Control, 61(3), 766–770. https://doi.org/10.1109/TAC.2015.2444051
   Web of Science ®Google Scholar
• Bachelier, O., Yeganefar, N., Mehdi, D., & Paszke, W. (2017). On stabilization of 2D roesser models. IEEE Transactions on Automatic Control, 62(5), 2505–2511. https://doi.org/10.1109/TAC.2016.2601238
   Web of Science ®Google Scholar
• Bamieh, B., Paganini, F., & Dalheh, M. A. (2002). Distributed control of spatially invariant systems. IEEE Transactions on Automatic Control, 47(7), 1091–1107. https://doi.org/10.1109/TAC.2002.800646
   Web of Science ®Google Scholar
• Bliman, P. A. (2004). An existence result for polynomial solutions of parameter dependent LMI. Systems and Control Letters, 52(3–4), 165–169. https://doi.org/10.1016/j.sysconle.2003.08.001
   Google Scholar
• Bose, N. K. (1982). Applied multidimensional system theory. Van Nostrand Reinhold Comp.
   Google Scholar
• Chesi, G. (2021). Exact LMI conditions for stability and L2 gain analysis of 2D mixed continuous-discrete-time systems via quadratically-frequency-dependent Lyapunov functions. IEEE Transactions on Automatic Control, 67(3), 1147–1162. https://doi.org/10.1109/TAC.2021.3065641.
   Web of Science ®Google Scholar
• Chesi, G., & Middleton, R. H. (2014). Necessary and sufficient LMI conditions for stability and performance analysis of 2D mixed continuous-discrete-time systems. IEEE Transactions on Automatic Control, 59(4), 996–1007. https://doi.org/10.1109/TAC.2014.2299353
   Web of Science ®Google Scholar
• Cichy, B., Augusta, P., Rogers, E., Gałkowski, K., & Hurak, Z. (2010). Robust control of distributed parameter mechanical systems using a multidimensional systems approach. Bulletin of The Polish Academy of Sciences -- Technical Sciences, 58(1), 67–75. https://doi.org/10.2478/v10175-010-0007-5
   Web of Science ®Google Scholar
• Curtain, R., & Zwart, H. J. (1995). An introduction to infinite-dimensional linear systems theory. Springer Verlag.
   Google Scholar
• D'Andrea, R., & Dullerud, G. E. (2003). Distributed control design for spatially interconnected systems. IEEE Transactions on Automatic Control, 48(9), 1478–1495. https://doi.org/10.1109/TAC.2003.816954
   Web of Science ®Google Scholar
• Dai, L. (1989). Singular control systems. Springer-Verlag.
   Google Scholar
• Gałkowski, K., & Wood, J. (2001). Multidimensional signals, circuits and systems. Taylor and Francis.
   Google Scholar
• Gorinevsky, D., & Stein, G. (2003). Structured uncertainty analysis of robust stability for multidimensional array systems. IEEE Transactions on Automatic Control, 48(9), 1557–1568. https://doi.org/10.1109/TAC.2003.816980
   Web of Science ®Google Scholar
• Hecker, S., & Varga, A. (2004). Generalized LFT-based representation of parametric models. European Journal of Control, 10(4), 326–337. https://doi.org/10.3166/ejc.10.326-337
   Web of Science ®Google Scholar
• Iwasaki, T., & Hara, S. (2005). Generalized KYP lemma : unified frequency domain inequalities with design applications. IEEE Transactions on Automatic Control, 50(1), 41–59. https://doi.org/10.1109/TAC.2004.840475
   Web of Science ®Google Scholar
• Kaczorek, T. (1985). Two dimensional linear systems, Lecture Notes in Control and Information Sciences, Vol. 68, Springer-Verlag.
   Google Scholar
• Li, L., Xu, L., & Lin, Z. (2013). Stability and stabilization of linear multidimensional discrete systems in the frequency domain. International Journal of Control, 86(11), 1969–1989. https://doi.org/10.1080/00207179.2013.823671
   Web of Science ®Google Scholar
• Mandra, S., Gałkowski, K., Rauh, A., Ascheman, A., & Rogers, E. (2021). Iterative learning control for a class of multivariable distributed systems with experimental validation. IEEE Transactions on Control Systems Technology, 29(3), 949–960. https://doi.org/10.1109/TCST.2020.2982612
   Web of Science ®Google Scholar
• Melzer, S. M., & Kuo, B. C. (1971). Optimal regulation of systems described by a countably infinite number of objects. Automatica, 7(3), 359–366. https://doi.org/10.1016/0005-1098(71)90128-2
   Web of Science ®Google Scholar
• Moore, K. L. (1993). Iterative learning control for deterministic systems, Avances in Industrial Control, Springer.
   Google Scholar
• Mosfegh, A. (1993). Discrete state-space modeling for linear nth-order constant coefficient distributed-parameter systems. Dynamics and Control, 3(1), 71–90. https://doi.org/10.1007/BF01968360
   Google Scholar
• Napp, D., Rapisarda, P., & Rocha, P. (2011). Time relevant stability of 2D systems. Automatica, 47(11), 2373–2382. https://doi.org/10.1016/j.automatica.2011.08.041
   Web of Science ®Google Scholar
• Oberst, U., & Scheicher, M. (2014). The asymptotic stability of stable and time-Autonomous discrete multidimensional behaviors. Mathematics of Control, Signals, and Systems, 26(2), 215–258. https://doi.org/10.1007/s00498-013-0114-6
   Web of Science ®Google Scholar
• Owens, D. H., Amann, N., Rogers, E., & French, M. (2000). Analysis of linear iterative learning control schemes -A 2D systems/Repetitive processes approach. Multidimensional Systems and Signal Processing, 11(1–2), 125–177. https://doi.org/10.1023/A:1008494815252
   Web of Science ®Google Scholar
• Peaucelle, D., Arzelier, D., Henrion, D., & Gouaisbault, F. (2007). Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation. Automatica, 43(5), 796–804. https://doi.org/10.1016/j.automatica.2006.11.005
   Web of Science ®Google Scholar
• Rajan, K. P., & Reddy, H. C. (1987). Modified Ansell's method and testing of very strict Hurwitz polynomials. IEEE Transactions on Circuits and Systems, 34(5), 559–561. https://doi.org/10.1109/TCS.1987.1086166
   Google Scholar
• Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10. https://doi.org/10.1109/TAC.1975.1100844
   Web of Science ®Google Scholar
• Rogers, E., Gałkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes, Vol. 349 of Lecture Notes in Control and Information Sciences. Springer-Verlag.
   Google Scholar
• Scherer, C. W. (2016). Lossless H ∞-synthesis for 2D systems. Systems and Control Letters, 95(9), 35–45. https://doi.org/10.1016/j.sysconle.2016.02.011
   Google Scholar
• Sulikowski, B., Gałkowski, K., Kummert, A, & Rogers, E. (2018). Two-dimensional (2D) systems approach to feedforward/feedback control of a class of spatially interconnected systems Distributed control design for spatially interconnected Markovian jump systems with time varying delays. International Journal of Control, (12), 2780–2791. https://doi.org/10.1080/00207179.2018.1522451
   Google Scholar