Keywords and phrases: state observer, 2-D state-delayed systems, linear matrix inequality (LMI), stability, Fornasini-Marchesini second model.
Received: December 7, 2022; Accepted: February 6, 2023; Published: February 20, 2023
How to cite this article: C. El-Kasri, M. Alfidi and A. Boua, Observer synthesis for 2-D discrete-time varying delays systems: F-M model, Advances and Applications in Discrete Mathematics 38(1) (2023), 29-47. http://dx.doi.org/10.17654/0974165823017
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] M. Alfidi, Z. Chalh and M. Ouahi, A constructive design of state observer for two-dimensional systems, WSEAS Transactions on Systems and Control 10 (2015), 430-435. [2] K. Badie, M. Alfidi and Z. Chalh, An LMI approach to design robust controller for 2-D systems with delays, Int. J. System of Systems Engineering 9(2) (2019), 99-116. [3] K. Badie, M. Alfidi, F. Tadeo and Z. Chalh, Delay-dependent stability and performance of 2-D continuous systems with delays, Circuits Systems Signal Process. 37(12) (2018), 5333-5350. [4] K. Badie, M. Alfidi and Z. Chalh, New relaxed stability conditions for uncertain two-dimensional discrete systems, Journal of Control, Automation and Electrical Systems 29(6) (2018), 661-669. [5] M. Bisiacco and M. E. Valcher, Observer-based fault detection and isolation for 2D state-space models, Multidimens. Syst. Signal Process. 17 (2006), 219-242. [6] M. Bisiacco and M. E. Valcher, Observer and Luenberger-type observers for 2D state-space models affected by unknown inputs, WSEAS Trans. Circuits Syst. 3 (2004), 1268-1273. [7] D. Chen and H. Yu, Stability analysis of state saturation 2D discrete time-delay systems based on F-M model, Math. Probl. Eng. 2013, Art. ID 749782, 9 pp. [8] S. F. Chen and I. K. Fong, Robust filtering for 2-D state-delayed systems with NFT uncertainties, IEEE Trans. Signal Process. 54 (2006), 274-285. [9] S.-F. Chen and I. K. Fong, Delay-dependent robust filtering for uncertain 2 D state-delayed systems signal, Processing 87(11) (2007), 2659-2672. [10] M. Elloumi, M. Ghamgui, D. Mehdi, F. Tadeo and M. Chaabane, Stability and stabilization of 2-D singular systems: a strict LMI approach, Circuits Systems Signal Process. 38 (2019), 3041-3057. [11] C. El-Kasri, A. Hmamed, T. Alvarez and F. Tadeo, Robust filtering of 2-D Roesser discrete systems: a polynomial approach, Math. Probl. Eng. 2012 (2012), 1-15. [12] C. El-Kasri, A. Hmamed, E. H. Tissir and F. Tadeo, Robust filtering for uncertain two-dimensional continuous systems with time-varying delays, Multidimens. Syst. Signal Process. 24(4) (2013), 685-706. [13] C. El-Kasri, A. Hmamed and F. Tadeo, Reduced-order filters for uncertain 2 D continuous systems, via LMIs and polynomial matrices, Circuits Systems Signal Process. 33(4) (2014), 1189-1214. [14] E. Fornasini and G. Marchesini, State-space realization theory of two-dimensional filters, IEEE Trans. Automat. Control 21 (1976), 484-492. [15] E. Fornasini and G. Marchesini, Doubly indexed dynamical systems state-space models and structural properties, Math. System Theory 12 (1978), 59-72. [16] L. V. Hien and H. Trinh, Observers design for 2-D positive time-delay Roesser systems, IEEE Transactions on Circuits and Systems II 65(4) (2018), 476-480. [17] L. V. Hien and H. Trinh, Delay-dependent stability and stabilization of two-dimensional positive Markov jump systems with delays, IET Control Theory Appl. 11(10) (2017), 1603-1610. [18] L. V. Hien and H. Trinh, Stability of two-dimensional Roesser systems with time-varying delays via novel 2-D finite-sum inequalities, IET Control Theory Appl. 10 (2016), 1665-1674. [19] T. Kaczorek, Two-dimensional linear systems, Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 1985. [20] D. H. Lee and Y. H. Joo, Extended robust and filter design for discrete time-invariant linear systems with polytopic uncertainty, Circuits Systems and Signal Processing 33(2) (2014), 393-419. [21] C. Li and M. S. Fadali, Optimal control of 2-D systems, IEEE Trans. Automat. Control 36 (1991), 223-228. [22] F. Long, C. K. Zhang, Y. He, L. Jiang, Q. G. Wang and M. Wu, Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality, Appl. Math. Comput. 328 (2018), 224-242. [23] W. S. Lu and A. Antoniou, Two-dimensional Digital Filters, New York, Marcel Dekker, 1992. [24] W. Marszalek, Two-dimensional state-space discrete models for hyperbolic partial differential equations, Appl. Math. Modeling 8 (1984), 11-14. [25] X. J. Ming and Y. Li, control for 2-D discrete state delayed systems in the second FM model, Acta Automat. Sinica 34(7) (2008), 809-813. [26] M. Oubaidi, Z. Chalh and M. Alfidi, Robust filtering of uncertain two-dimensional discrete systems with delays, International Journal of Innovative Computing, Information and Control 17(1) (2021), 315-333. [27] R. P. Roesser, A discrete state-space model for linear image processing, IEEE Trans. Automat. Control 20(1) (1975), 1-10. [28] Y. Shen, L. Wang, J. Yub, R. Zhang and F. Gaoc, A hybrid 2-D fault-tolerant controller design for multi-phase batch processes with time delay, Journal of Process Control 69 (2018), 138-157. [29] J. S.-H. Tsai, J. S. Li and L.-S. Shieh, Discretized quadratic optimal control for continuous time two dimensional systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49 (2002), 116-125. [30] S. G. Tzafestas, A. Kanellakis and N. J. Theodorou, Two-dimensional digital filters without overflow oscillations and instability due to finite word length, IEEE Trans. Signal Process. 40(9) (1992), 2311-2317. [31] H. Xu and Y. Zou, Robust filtering for uncertain two-dimensional discrete systems with state-varying delays, Int. J. of Control, Automation and Systems 8(4) (2010), 720-726. [32] X. M. Zhang and Q. L. Han, Event-triggered dynamic output feedback control for networked control systems, IET Control Theory Appl. 8 (2014), 226-234. [33] C. Zhou, J. He and Q. Chen, A robust active queue management scheme for network congestion control, Comput. Electr. Eng. 39(2) (2013), 285-294.
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