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International Journal of Control Volume 86, 2013 - Issue 11: Systems, Modelling and Feedback Control: A Special Issue Dedicated to Sir Alistair G.J. MacFarlane
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Original Articles

Stability and stabilisation of linear multidimensional discrete systems in the frequency domain

Lizhen Li Department of Science, Nanjing University of Science and Technology, Nanjing, 210094, China
,
Li Xu Faculty of Systems Science and Technology, Akita Prefectural University, Akita, 015-0055, Japan
&
Zhiping Lin School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore
Pages 1969-1989 | Received 09 Feb 2013, Accepted 07 Jul 2013, Published online: 15 Oct 2013

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Souad Salmi & Djillali Bouagada. (2024) Stability robust for fractional generalized multi-dimensional state–space models. International Journal of Computer Mathematics 101:4, pages 432-446.
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O. Bachelier, T. Cluzeau, A. Rigaud, F. J. Silva Alvarez & N. Yeganefar. (2023) On exponential stability of a class of descriptor continuous linear 2D Roesser models. International Journal of Control 96:6, pages 1582-1593.
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Mariem Ghamgui, Driss Mehdi, Olivier Bachelier & Mohamed Chaabane. (2018) On the robust state-feedback stabilisation of nD hybrid Roesser models with implicit LFR uncertainty. International Journal of Control 91:12, pages 2705-2713.
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Olivier Bachelier, Thomas Cluzeau, Ronan David, Francisco José Silva Álvarez, Nader Yeganefar & Nima Yeganefar. (2018) Structural stability, asymptotic stability and exponential stability for linear multidimensional systems: the good, the bad and the ugly. International Journal of Control 91:12, pages 2714-2725.
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Olivier Bachelier, Thomas Cluzeau, Alexandre Rigaud, Francisco José Silva Alvarez, Nader Yeganefar & Nima Yeganefar. (2023) On the Connections Between Various Stability Notions for Linear 2-D Discrete Models. IEEE Transactions on Automatic Control 68:12, pages 7919-7926.
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Apostolos Kanellakis & Ayman Tawfik. (2023) Sufficient criterion for instability of 2-D linear discrete systems. Franklin Open 3, pages 100019.
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Bossoto Bossoto, Mamadou Mboup & Alain Yger. (2023) Amœbas and structural stability of multidimensional systems: a test algorithm based on Monte-Carlo integration. Multidimensional Systems and Signal Processing 34:2, pages 479-502.
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Olivier Bachelier, Thomas Cluzeau, Alexandre Rigaud, Francisco Jose Silva Alvarez & Nima Yeganefar. (2022) Equivalence between different stability definitions for 2D linear discrete Roesser models. Equivalence between different stability definitions for 2D linear discrete Roesser models.
Zhen Zhu, Jun-Guo Lu & Qing-Hao Zhang. (2022) LMI-Based Stability Analysis of Continuous-Discrete Fractional-Order 2D Roesser Model. IEEE Transactions on Circuits and Systems II: Express Briefs 69:6, pages 2797-2801.
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Yuval Bistritz. (2021) Bounded-Input Bounded-Output Stability Tests for Two-Dimensional Continuous-Time Systems. IEEE Transactions on Circuits and Systems I: Regular Papers 68:5, pages 2134-2147.
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Reza Mohsenipour & Panajotis Agathoklis. (2021) Algebraic Necessary and Sufficient Conditions for Testing Stability of 2-D Linear Systems. IEEE Transactions on Automatic Control 66:4, pages 1825-1831.
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Olivier Bachelier, Thomas Cluzeau, Driss Mehdi & Nima Yeganefar. (2021) New Tests for the Stability of 2-D Roesser Models. IEEE Transactions on Automatic Control 66:1, pages 406-412.
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Apostolos Kanellakis & Ayman Tawfik. (2021) A New Sufficient Criterion for the Stability of 2-D Discrete Systems. IEEE Access 9, pages 70392-70395.
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Frantisek J. Kraus & Panajotis Agathoklis. (2020) Stability Testing of 2D Filters Based on Tschebyscheff Polynomials and Generalized Eigenvalues. Stability Testing of 2D Filters Based on Tschebyscheff Polynomials and Generalized Eigenvalues.
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Shi Yan, Dongdong Zhao, Hai Wang, Shinya Matsushita & Li Xu. (2020) A novel constructive procedure to low-order Fornasini–Marchesini model realization. Journal of the Franklin Institute 357:3, pages 1764-1789.
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Y. Bouzidi, A. Quadrat & F. Rouillier. (2018) Certified non-conservative tests for the structural stability of discrete multidimensional systems. Multidimensional Systems and Signal Processing 30:3, pages 1205-1235.
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Olivier Bachelier, Thomas Cluzeau, Driss Mehdi & Nima Yeganefar. (2019) New LMI conditions for the stability of 2D discrete Roesser models. New LMI conditions for the stability of 2D discrete Roesser models.
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Olivier Bachelier, Wojciech Paszke, Nima Yeganefar & Driss Mehdi. (2018) Comments on “On Stabilization of 2-D Roesser Models”. IEEE Transactions on Automatic Control 63:8, pages 2745-2749.
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Sameh Ben Mohamed, Boumedyen Boussaid, Mohamed Naceur Abdelkrim & Charfeddine Tahri. (2017) 1D and 2D modelling of a chemical process using the FM-II model: Rotary drum filter. Transactions of the Institute of Measurement and Control 40:4, pages 1309-1319.
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Olivier Bachelier, Thomas Cluzeau, Ronan David & Nima Yeganefar. (2016) Structural stabilization of linear 2D discrete systems using equivalence transformations. Multidimensional Systems and Signal Processing 28:4, pages 1629-1652.
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Olivier Bachelier, Thomas Cluzeau, Ronan David & Nima Yeganefar. (2017) An Algebraic Approach to the Observer-Based Feedback Stabilization of Linear 2D Discrete Models. IFAC-PapersOnLine 50:1, pages 1859-1864.
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R. David, O. Bachelier, T. Cluzeau, F. Silva, Na. Yeganefar & Ni. Yeganefar. (2017) Structural Stability and Asymptotic Stability for Linear Multidimensional Systems: a Counterexample * *This work was supported by the ANR MSDOS grant ANR-13-BS03-0005.. IFAC-PapersOnLine 50:1, pages 1853-1858.
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Olivier Bachelier, Nima Yeganefar, Driss Mehdi & Wojciech Paszke. (2017) On Stabilization of 2D Roesser Models. IEEE Transactions on Automatic Control 62:5, pages 2505-2511.
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Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov & Hugo J. Woerdeman. (2015) Contractive determinantal representations of stable polynomials on a matrix polyball. Mathematische Zeitschrift 283:1-2, pages 25-37.
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Ju-Hong Lee & Jiun-Shian Du. (2016) Phase Characteristics for the Stability of 2-D Quarter-Plane Recursive Digital All-Pass Filters. IEEE Transactions on Circuits and Systems II: Express Briefs 63:3, pages 289-293.
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Olivier Bachelier, Wojciech Paszke, Nima Yeganefar, Driss Mehdi & Abdelmadjid Cherifi. (2016) LMI Stability Conditions for 2D Roesser Models. IEEE Transactions on Automatic Control 61:3, pages 766-770.
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Olivier Bachelier, Ronan David, Nima Yeganefar & Thomas Cluzeau. (2016) Structural Stability and Equivalence of Linear 2D Discrete Systems11This work was supported by the ANR-13-BS03-0005 (MSDOS).. IFAC-PapersOnLine 49:9, pages 136-141.
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Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov & Hugo J. Woerdeman. (2014) Stable and real-zero polynomials in two variables. Multidimensional Systems and Signal Processing 27:1, pages 1-26.
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Dong Zhao, Donghua Zhou & Youqing Wang. (2015) Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation. Multidimensional Systems and Signal Processing 26:4, pages 1061-1080.
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Eva Zerz & Sebastian Walcher. (2015) nD methods for 1D parameter-dependent systems. Multidimensional Systems and Signal Processing 26:4, pages 1097-1108.
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Yacine Bouzidi, Alban Quadrat & Fabrice Rouillier. (2015) Computer algebra methods for testing the structural stability of multidimensional systems. Computer algebra methods for testing the structural stability of multidimensional systems.
Olivier Bachelier, Nima Yeganefar, Driss Mehdi & Wojciech Paszke. (2015) State feedback structural stabilization of 2D discrete Roesser models. State feedback structural stabilization of 2D discrete Roesser models.
Dong Zhao & Youqing Wang. (2015) Integrated Fault Detection for Two-Dimensional Discrete Systems with Time-Varying Delays. IFAC-PapersOnLine 48:21, pages 1262-1267.
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Dong Zhao, Youqing Wang & Bin Zhang. (2014) Unknown input observer for 2-D Fornasini-Marchesini system using descriptor system approach. Unknown input observer for 2-D Fornasini-Marchesini system using descriptor system approach.

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