We develop algebraic, effective, and symbolic-numeric methods dedicated to problems studied in control theory and signal processing. More precisely, we combine methods of algebraic analysis, algebraic geometry, and computer algebra to study analysis and synthesis problems such as the effective study of structural properties of linear functional systems, equivalence problems, symbolic-numeric methods for stability analysis and robust stabilization problems for multidimensional systems and infinite-dimensional systems (e.g., differential time-delay systems, partial differential systems), as well as for parameter estimation, demodulation problems, and geolocalization problem.

We develop symbolic packages (prototypes) in Maple, Mathematica, GAP, etc., based on our results.

We collaborate with Safran Electronics & Defense and Safran Tech companies on some of these problems.

**Publications on the algebraic analysis approach to linear systems theory**

- A. Quadrat, “An Integro-differential Operator Approach to Linear State-space Systems,” in SSSC 2022 – 8th IFAC Symposium on System Structure and Control, Montreal, Canada, 2022.

[Bibtex]`@inproceedings{quadrat:hal-03908550, TITLE = {{An Integro-differential Operator Approach to Linear State-space Systems}}, AUTHOR = {Quadrat, Alban}, URL = {https://inria.hal.science/hal-03908550}, BOOKTITLE = {{SSSC 2022 - 8th IFAC Symposium on System Structure and Control}}, ADDRESS = {Montreal, Canada}, YEAR = {2022}, MONTH = Sep, DOI = {10.1016/j.ifacol.2022.11.299}, KEYWORDS = {Linear systems ; Continuous-time linear state-space models ; Polynomial methods ; Algebraic analysis ; Rings of integro-differential operators ; System equivalence ; Behaviours}, PDF = {https://inria.hal.science/hal-03908550/file/main_final.pdf}, HAL_ID = {hal-03908550}, HAL_VERSION = {v1}, }`

- A. Quadrat, “An Integro-differential-delay Operator Approach to Transformations of Linear Differential Time-delay Systems,” in SSSC 2022 – 8th IFAC Symposium on System Structure and Control, Montréal, Canada, 2022.

[Bibtex]`@inproceedings{quadrat:hal-03908561, TITLE = {{An Integro-differential-delay Operator Approach to Transformations of Linear Differential Time-delay Systems}}, AUTHOR = {Quadrat, Alban}, URL = {https://inria.hal.science/hal-03908561}, BOOKTITLE = {{SSSC 2022 - 8th IFAC Symposium on System Structure and Control}}, ADDRESS = {Montr{\'e}al, Canada}, YEAR = {2022}, MONTH = Sep, DOI = {10.1016/j.ifacol.2022.11.301}, KEYWORDS = {Linear systems ; Systems with time-delays ; Polynomial methods ; Delay compensation}, PDF = {https://inria.hal.science/hal-03908561/file/Integro-diff-delay-final-reduced_corrected.pdf}, HAL_ID = {hal-03908561}, HAL_VERSION = {v1}, }`

- A. Quadrat, “An integro-differential operator approach to linear differential systems,” in MTNS 2022 – 25th International Symposium on Mathematical Theory of Networks and Systems, Bayreuth, Germany, 2022.

[Bibtex]`@inproceedings{quadrat:hal-03908541, TITLE = {{An integro-differential operator approach to linear differential systems}}, AUTHOR = {Quadrat, Alban}, URL = {https://inria.hal.science/hal-03908541}, BOOKTITLE = {{MTNS 2022 - 25th International Symposium on Mathematical Theory of Networks and Systems}}, ADDRESS = {Bayreuth, Germany}, YEAR = {2022}, MONTH = Sep, DOI = {10.1016/j.ifacol.2022.11.054}, KEYWORDS = {Linear systems ; Polynomial methods ; Algebraic analysis ; Rings of integro-differential operators ; Parametrization ; Reachability ; Behaviour theory}, PDF = {https://inria.hal.science/hal-03908541/file/MTNS_final.pdf}, HAL_ID = {hal-03908541}, HAL_VERSION = {v1}, }`

- A. Quadrat and R. Ushirobira, “On the Ore extension ring of differential time-varying delay operators,” in Accounting for Constraints in Delay Systems, Advances in Delays and Dynamics (ADD), volume 12, Springer, pp. 87-107, Springer, 2022, vol. ADD-2, p. pp. 87-107.

[Bibtex]`@incollection{quadrat:hal-03908643, TITLE = {{On the Ore extension ring of differential time-varying delay operators}}, AUTHOR = {Quadrat, Alban and Ushirobira, Rosane}, URL = {https://inria.hal.science/hal-03908643}, BOOKTITLE = {{Accounting for Constraints in Delay Systems, Advances in Delays and Dynamics (ADD), volume 12, Springer, pp. 87-107}}, PUBLISHER = {{Springer}}, SERIES = {Advances in Delays and Dynamics}, VOLUME = {ADD-2}, PAGES = {pp. 87-107}, YEAR = {2022}, MONTH = Apr, DOI = {10.1007/978-3-030-89014-8\_5}, PDF = {https://inria.hal.science/hal-03908643/file/decod-2018-final.pdf}, HAL_ID = {hal-03908643}, HAL_VERSION = {v1}, }`

- A. Quadrat and E. Zerz, Algebraic and Symbolic Computation Methods in Dynamical Systems, E. Z. Alban Quadrat, Ed., Springer, 2020, vol. 9.

[Bibtex]`@book{quadrat:hal-03070784, TITLE = {{Algebraic and Symbolic Computation Methods in Dynamical Systems}}, AUTHOR = {Quadrat, Alban and Zerz, Eva}, URL = {https://inria.hal.science/hal-03070784}, EDITOR = {Alban Quadrat, Eva Zerz}, PUBLISHER = {{Springer}}, SERIES = {Advances in Delays and Dynamics}, VOLUME = {9}, PAGES = {311}, YEAR = {2020}, DOI = {10.1007/978-3-030-38356-5}, KEYWORDS = {Algebraic Theories ; Control Theory ; Computer Algebra System ; Symbolic Computation Method ; Algebraic Computation Methods}, HAL_ID = {hal-03070784}, HAL_VERSION = {v1}, }`

- T. Cluzeau, C. Koutschan, A. Quadrat, and M. Tõnso, “Effective algebraic analysis approach to linear systems over Ore algebras,” in Algebraic and Symbolic Computation Methods in Dynamical Systems, Springer, 2020, vol. 9, pp. 4-52.

[Bibtex]`@incollection{cluzeau:hal-02436985, TITLE = {{Effective algebraic analysis approach to linear systems over Ore algebras}}, AUTHOR = {Cluzeau, Thomas and Koutschan, Christoph and Quadrat, Alban and Tõnso, Maris}, URL = {https://hal.science/hal-02436985}, BOOKTITLE = {{Algebraic and Symbolic Computation Methods in Dynamical Systems}}, PUBLISHER = {{Springer}}, SERIES = {Advances in Delays and Dynamics}, VOLUME = {9}, PAGES = {4-52}, YEAR = {2020}, HAL_ID = {hal-02436985}, HAL_VERSION = {v1}, }`

- T. Cluzeau and A. Quadrat, “Equivalences of linear functional systems,” in Algebraic Methods and Symbolic-Numeric Computation in Systems Theory, Springer, 2020, vol. 9, pp. 53-86.

[Bibtex]`@incollection{cluzeau:hal-03070672, TITLE = {{Equivalences of linear functional systems}}, AUTHOR = {Cluzeau, Thomas and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03070672}, BOOKTITLE = {{Algebraic Methods and Symbolic-Numeric Computation in Systems Theory}}, PUBLISHER = {{Springer}}, VOLUME = {9}, PAGES = {53-86}, YEAR = {2020}, KEYWORDS = {Linear systems theory ; Equivalence problem ; Control theory ; Algebraic analysis ; Computer algebra}, HAL_ID = {hal-03070672}, HAL_VERSION = {v1}, }`

**Publications on the parameter estimation problems**

- M. Chartouny, T. Cluzeau, and A. Quadrat, “Algorithmic study of the algebraic parameter estimation problem for a class of perturbations,” Maple Transactions, vol. 3, 2023.

[Bibtex]`@article{chartouny:hal-04203089, TITLE = {{Algorithmic study of the algebraic parameter estimation problem for a class of perturbations}}, AUTHOR = {Chartouny, Maya and Cluzeau, Thomas and Quadrat, Alban}, URL = {https://inria.hal.science/hal-04203089}, JOURNAL = {{Maple Transactions}}, PUBLISHER = {{Western Libraries Western University}}, VOLUME = {3}, YEAR = {2023}, MONTH = Feb, DOI = {10.5206/mt.v2i2.14467}, KEYWORDS = {Parameter estimation problem ; Inverse Cauchy problem ; Algebraic systems ; Elimination ; Annihilators ; Rings of ordinary differential operators}, PDF = {https://inria.hal.science/hal-04203089/file/CCQ_MapleTransactionsFinal-1.pdf}, HAL_ID = {hal-04203089}, HAL_VERSION = {v1}, }`

- M. Chartouny, T. Cluzeau, and A. Quadrat, “On the inverse Cauchy problem for linear ordinary differential equations,” in GAMM 2021 – 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Kassel, Germany, 2021.

[Bibtex]`@inproceedings{chartouny:hal-03530281, TITLE = {{On the inverse Cauchy problem for linear ordinary differential equations}}, AUTHOR = {Chartouny, Maya and Cluzeau, Thomas and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03530281}, BOOKTITLE = {{GAMM 2021 - 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics}}, ADDRESS = {Kassel, Germany}, EDITOR = {Wiley}, SERIES = {Applied Mathematics and Mechanics PAMM 2021}, VOLUME = {21}, NUMBER = {1}, YEAR = {2021}, MONTH = Mar, DOI = {10.1002/pamm.202100214}, PDF = {https://inria.hal.science/hal-03530281/file/GAMM_Alban.pdf}, HAL_ID = {hal-03530281}, HAL_VERSION = {v1}, }`

**Publications on the demodulation problems arising in vibration analysis (collaboration with Safran Tech)**

- R. Dagher, E. Hubert, and A. Quadrat, “On the general solutions of a rank factorization problem,” {Sobonne Université, IMJ – PRG, Inria Paris ; Inria Lille – Nord Europe ; Laboratoire d’Analyse des Signaux et Processus Industriels}, Research Report RR-9438, 2021.

[Bibtex]`@techreport{dagher:hal-03479643, TITLE = {{On the general solutions of a rank factorization problem}}, AUTHOR = {Dagher, Roudy and Hubert, Elisa and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03479643}, TYPE = {Research Report}, NUMBER = {RR-9438}, PAGES = {57}, INSTITUTION = {{Sobonne Universit{\'e}, IMJ - PRG, Inria Paris ; Inria Lille - Nord Europe ; Laboratoire d'Analyse des Signaux et Processus Industriels}}, YEAR = {2021}, MONTH = Dec, KEYWORDS = {Vibration analysis ; Gearbox fault detection/surveillance ; Demodulation problems ; Homological algebra ; Module theory ; Centrohermitian matrix ; Rank factorization problem ; Polynomial systems ; Analyse vibratoire ; D{\'e}tection et surveillance des d{\'e}fauts d'engrenages ; Probl{\`e}mes de d{\'e}modulation ; Alg{\`e}bre homologique ; Th{\'e}orie des modules ; Matrice centrohermitiennes ; Factorisation relative au rang ; Syst{\`e}mes polynomiaux}, PDF = {https://inria.hal.science/hal-03479643v2/file/RR-9438-v2.pdf}, HAL_ID = {hal-03479643}, HAL_VERSION = {v2}, }`

- Y. Bouzidi, R. Dagher, E. Hubert, and A. Quadrat, “Algebraic aspects of a rank factorization problem arising in vibration analysis,” Communications in Computer and Information Science, vol. 1414, 2021.

[Bibtex]`@article{bouzidi:hal-03529914, TITLE = {{Algebraic aspects of a rank factorization problem arising in vibration analysis}}, AUTHOR = {Bouzidi, Yacine and Dagher, Roudy and Hubert, Elisa and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03529914}, JOURNAL = {{Communications in Computer and Information Science}}, EDITOR = {Corless R.M. and Gerhard J. and Kotsireas I.S}, PUBLISHER = {{Springer}}, SERIES = {Maple in Mathematics Education and Research}, VOLUME = {1414}, YEAR = {2021}, MONTH = Jan, DOI = {10.1007/978-3-030-81698-8\_8}, KEYWORDS = {Gearbox vibration signals ; Demodulation problems ; Effective module theory ; Polynomial systems}, PDF = {https://inria.hal.science/hal-03529914/file/Maple2020.pdf}, HAL_ID = {hal-03529914}, HAL_VERSION = {v1}, }`

- E. Hubert, Y. Bouzidi, R. Dagher, and A. Quadrat, “Centrohermitian solutions of a factorization problem arising in vibration analysis. Part I: Lee’s transformation,” in ECC 2021 – European Control Conference, Delft (Virtual), Netherlands, 2021.

[Bibtex]`@inproceedings{hubert:hal-03530244, TITLE = {{Centrohermitian solutions of a factorization problem arising in vibration analysis. Part I: Lee's transformation}}, AUTHOR = {Hubert, Elisa and Bouzidi, Yacine and Dagher, Roudy and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03530244}, BOOKTITLE = {{ECC 2021 - European Control Conference}}, ADDRESS = {Delft (Virtual), Netherlands}, YEAR = {2021}, MONTH = Jun, DOI = {10.23919/ECC54610.2021.9655069}, KEYWORDS = {Polynomial systems ; Effective module theory ; Demodulation problems ; Gearbox vibration signals ; Centrohermitian matrix}, PDF = {https://inria.hal.science/hal-03530244/file/Centrohermitian_final.pdf}, HAL_ID = {hal-03530244}, HAL_VERSION = {v1}, }`

- E. Hubert, Y. Bouzidi, R. Dagher, and A. Quadrat, “Centrohermitian Solutions of a Factorization Problem Arising in Vibration Analysis. Part II: A Coninvolutory Matrix Approach,” in ECC 2021 – European Control Conference, Delft (Virtual), Netherlands, 2021.

[Bibtex]`@inproceedings{hubert:hal-03530258, TITLE = {{Centrohermitian Solutions of a Factorization Problem Arising in Vibration Analysis. Part II: A Coninvolutory Matrix Approach}}, AUTHOR = {Hubert, Elisa and Bouzidi, Yacine and Dagher, Roudy and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03530258}, BOOKTITLE = {{ECC 2021 - European Control Conference}}, ADDRESS = {Delft (Virtual), Netherlands}, YEAR = {2021}, MONTH = Jun, DOI = {10.23919/ECC54610.2021.9655115}, KEYWORDS = {Demodulation problems ; Gearbox vibration signals ; Centrohermitian matrix ; Polynomial systems ; Effective module theory}, PDF = {https://inria.hal.science/hal-03530258/file/Centrohermitian_Part2_final.pdf}, HAL_ID = {hal-03530258}, HAL_VERSION = {v1}, }`

- E. Hubert, A. Barrau, Y. Bouzidi, R. Dagher, and A. Quadrat, “Algebraic aspects of a rank factorization problem arising in vibration analysis,” in Maple Conference, Waterloo / Virtual, Canada, 2020.

[Bibtex]`@inproceedings{hubert:hal-03070709, TITLE = {{Algebraic aspects of a rank factorization problem arising in vibration analysis}}, AUTHOR = {Hubert, Elisa and Barrau, Axel and Bouzidi, Yacine and Dagher, Roudy and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03070709}, BOOKTITLE = {{Maple Conference}}, ADDRESS = {Waterloo / Virtual, Canada}, YEAR = {2020}, MONTH = Nov, HAL_ID = {hal-03070709}, HAL_VERSION = {v1}, }`

- E. Hubert, A. Barrau, Y. Bouzidi, R. Dagher, and A. Quadrat, “On a rank factorisation problem arising in gearbox vibration analysis,” in IFAC 2020 – 21st World Congress, Berlin / Virtual, Germany, 2020.

[Bibtex]`@inproceedings{hubert:hal-03070702, TITLE = {{On a rank factorisation problem arising in gearbox vibration analysis}}, AUTHOR = {Hubert, Elisa and Barrau, Axel and Bouzidi, Yacine and Dagher, Roudy and Quadrat, Alban}, URL = {https://inria.hal.science/hal-03070702}, BOOKTITLE = {{IFAC 2020 - 21st World Congress}}, ADDRESS = {Berlin / Virtual, Germany}, YEAR = {2020}, MONTH = Jul, KEYWORDS = {Demodulation ; Modulation ; Factorisation methods ; Vibration analysis ; Linear algebra}, PDF = {https://inria.hal.science/hal-03070702v2/file/IFAC_2020_final.pdf}, HAL_ID = {hal-03070702}, HAL_VERSION = {v2}, }`

- E. Hubert, Y. Bouzidi, R. Dagher, A. Barrau, and A. Quadrat, “Algebraic aspects of the exact signal demodulation problem,” in SSSC 2019 – 7th IFAC Symposium on Systems Structure and Control, Sinaia, Romania, 2019.

[Bibtex]`@inproceedings{hubert:hal-02419824, TITLE = {{Algebraic aspects of the exact signal demodulation problem}}, AUTHOR = {Hubert, Elisa and Bouzidi, Yacine and Dagher, Roudy and Barrau, Axel and Quadrat, Alban}, URL = {https://inria.hal.science/hal-02419824}, BOOKTITLE = {{SSSC 2019 - 7th IFAC Symposium on Systems Structure and Control}}, ADDRESS = {Sinaia, Romania}, YEAR = {2019}, MONTH = Sep, DOI = {10.1016/j.ifacol.2019.11.031}, KEYWORDS = {Homological algebra ; Demodulation ; Linear systems ; Polynomial systems}, HAL_ID = {hal-02419824}, HAL_VERSION = {v1}, }`

**Publications on the algebraic geometric aspects to analysis and synthesis problems**

- G. Younes, “Computation of the L$\infty$-norm of finite-dimensional linear systems,” Theses PhD Thesis, 2022.

[Bibtex]`@phdthesis{younes:tel-03863650, TITLE = {{Computation of the L$\infty$-norm of finite-dimensional linear systems}}, AUTHOR = {Younes, Grace}, URL = {https://theses.hal.science/tel-03863650}, NUMBER = {2022SORUS125}, SCHOOL = {{Sorbonne Universit{\'e}}}, YEAR = {2022}, MONTH = Jan, KEYWORDS = {L$\infty$ norm computation ; Polynomial systems ; Maximal real roots ; Symbolicla computation ; Complexity computation ; Control theory ; Implementation ; Calcul de la norme L$\infty$ ; Syst{\`e}mes polynomiaux ; Solutions r{\'e}elles maximales ; Calcul symbolique ; Calcul de complexit{\'e} ; Th{\'e}orie du contr{\^o}le ; Impl{\'e}mentation}, TYPE = {Theses}, PDF = {https://theses.hal.science/tel-03863650/file/YOUNES_Grace_these_2022.pdf}, HAL_ID = {tel-03863650}, HAL_VERSION = {v1}, }`

- Y. Bouzidi, A. Quadrat, F. Rouillier, and G. Younes, “Computation of the $\mathcal{L} \infty$ -norm of finite-dimensional linear systems,” Communications in Computer and Information Science, 2021.

[Bibtex]`@article{bouzidi:hal-03328685, TITLE = {{Computation of the $\mathcal{L} \infty$ -norm of finite-dimensional linear systems}}, AUTHOR = {Bouzidi, Yacine and Quadrat, Alban and Rouillier, Fabrice and Younes, Grace}, URL = {https://inria.hal.science/hal-03328685}, JOURNAL = {{Communications in Computer and Information Science}}, PUBLISHER = {{Springer Verlag}}, YEAR = {2021}, MONTH = Aug, KEYWORDS = {$\mathcal{L}\infty$-norm computation ; Real roots ; Symbolic computation ; Complexity computation ; Implementation ; Control theory}, PDF = {https://inria.hal.science/hal-03328685/file/Infinity_norm.pdf}, HAL_ID = {hal-03328685}, HAL_VERSION = {v1}, }`

- Y. Bouzidi, A. Quadrat, F. Rouillier, and G. Younes, “Computation of the $\mathcal{L}_{\infty}$-norm of finite-dimensional linear systems,” in Maple Conference, Waterloo, Canada, 2020.

[Bibtex]`@inproceedings{bouzidi:hal-03073801, TITLE = {{Computation of the $\mathcal{L}\_{\infty}$-norm of finite-dimensional linear systems}}, AUTHOR = {Bouzidi, Yacine and Quadrat, Alban and Rouillier, Fabrice and Younes, Grace}, URL = {https://inria.hal.science/hal-03073801}, BOOKTITLE = {{Maple Conference}}, ADDRESS = {Waterloo, Canada}, YEAR = {2020}, MONTH = Nov, HAL_ID = {hal-03073801}, HAL_VERSION = {v1}, }`

- Y. Bouzidi, T. Cluzeau, A. Quadrat, and F. Rouillier, “On the effective computation of stabilizing controllers of 2D systems,” in Maple in Mathematics Education and Research, I. K. Jürgen Gerhard, Ed., Springer, 2020, vol. Maple in Mathematics Education and Research, pp. 30-49.

[Bibtex]`@incollection{bouzidi:hal-03070677, TITLE = {{On the effective computation of stabilizing controllers of 2D systems}}, AUTHOR = {Bouzidi, Yacine and Cluzeau, Thomas and Quadrat, Alban and Rouillier, Fabrice}, URL = {https://inria.hal.science/hal-03070677}, BOOKTITLE = {{Maple in Mathematics Education and Research}}, EDITOR = {J{\"u}rgen Gerhard, Ilias Kotsireas}, PUBLISHER = {{Springer}}, VOLUME = {Maple in Mathematics Education and Research}, PAGES = {30-49}, YEAR = {2020}, HAL_ID = {hal-03070677}, HAL_VERSION = {v1}, }`

- Y. Bouzidi and F. Rouillier, “Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability,” in Algebraic and Symbolic Computation Methods in Dynamical Systems, A. Quadrat and E. Zerz, Eds., Springer, 2020, pp. 203-237.

[Bibtex]`@incollection{bouzidi:hal-02907338, TITLE = {{Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability}}, AUTHOR = {Bouzidi, Yacine and Rouillier, Fabrice}, URL = {https://inria.hal.science/hal-02907338}, BOOKTITLE = {{Algebraic and Symbolic Computation Methods in Dynamical Systems}}, EDITOR = {Alban Quadrat and Eva Zerz}, PUBLISHER = {{Springer}}, PAGES = {203-237}, YEAR = {2020}, MONTH = May, DOI = {10.1007/978-3-030-38356-5\_8}, PDF = {https://inria.hal.science/hal-02907338/file/chapitre_springer.pdf}, HAL_ID = {hal-02907338}, HAL_VERSION = {v1}, }`

- Y. Bouzidi, T. Cluzeau, A. Quadrat, and F. Rouillier, “On the effective computation of stabilizing controllers of 2D systems,” in Maple Conference, Waterloo, Canada, 2019, p. 19.

[Bibtex]`@inproceedings{bouzidi:hal-02419719, TITLE = {{On the effective computation of stabilizing controllers of 2D systems}}, AUTHOR = {Bouzidi, Yacine and Cluzeau, Thomas and Quadrat, Alban and Rouillier, Fabrice}, URL = {https://inria.hal.science/hal-02419719}, BOOKTITLE = {{Maple Conference}}, ADDRESS = {Waterloo, Canada}, EDITOR = {Juergen Gerhart and Ilias Kotsireas}, PUBLISHER = {{Springer International Publishing}}, SERIES = {Maple in Mathematics Education and Research}, VOLUME = {1125}, PAGES = {19}, YEAR = {2019}, MONTH = Oct, DOI = {10.1007/978-3-030-41258-6\_3}, PDF = {https://inria.hal.science/hal-02419719/file/Stabilization_2D.pdf}, HAL_ID = {hal-02419719}, HAL_VERSION = {v1}, }`

- Y. M. Bouzidi, A. Quadrat, and F. Rouillier, “Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems,” Multidimensional Systems and Signal Processing, vol. 30, iss. 3, p. 31, 2019.

[Bibtex]`@article{bouzidi:hal-01951765, TITLE = {{Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems}}, AUTHOR = {Bouzidi, Yacine Mohamed and Quadrat, Alban and Rouillier, Fabrice}, URL = {https://inria.hal.science/hal-01951765}, JOURNAL = {{Multidimensional Systems and Signal Processing}}, PUBLISHER = {{Springer Verlag}}, VOLUME = {30}, NUMBER = {3}, PAGES = {31}, YEAR = {2019}, MONTH = Jul, DOI = {10.1007/s11045-018-0596-y}, KEYWORDS = {Multidimensional systems ; Computer algebra ; Structural stability ; Stability analysis}, PDF = {https://inria.hal.science/hal-01951765/file/Stability_nD.pdf}, HAL_ID = {hal-01951765}, HAL_VERSION = {v1}, }`

**Patent**

R. Dagher, A. Quadrat, G. Zheng, Auto-localisation par mesure de distances, WO2019207238A1, Inria France, 2018 FR, 2019 EP US WO CN KR JP

- R. Dagher, G. Zheng, and A. Quadrat, General closed-form solutions of the position self-calibration problem, 2019.

[Bibtex]`@misc{dagher:hal-02419854, TITLE = {{General closed-form solutions of the position self-calibration problem}}, AUTHOR = {Dagher, Roudy and Zheng, Gang and Quadrat, Alban}, URL = {https://inria.hal.science/hal-02419854}, NOTE = {Paper under submission}, YEAR = {2019}, MONTH = Oct, HAL_ID = {hal-02419854}, HAL_VERSION = {v1}, }`

**Packages**

OreModules A symbolic package for the study of linear functional systems over Ore algebras (*Maple*)

OreMorphisms A homological algebra package for factoring, reducing and decomposing linear functional systems (*Maple*)

OreAlgebraicAnalysis A *Mathematica* implementation of the OreModules and OreMorphisms packages (*Mathematica*)

QuillenSuslin A package dedicated to the Quillen-Suslin theorem and its applications (*Maple*)

Stafford A package dedicated to Stafford’s results on Weyl algebras and their applications (*Maple*)

PurityFiltration A package dedicated to the the computation of purity (codimension/bidualizing) filtration of modules and reduction to equidimensional block-triangular forms (*Maple*)

NonA A symbolic package dedicated to the algebraic parameter estimation problem (*Maple*)

RankFactorization A package dedicated to effective study of the rank factorization problem and its applications to vibration analysis (*Maple*) (see Appendix of the second version (2023) of the paper)

**Foundational publications**

A. Quadrat, On a generalization of the Youla-Kucera parametrization. II. The lattice approach to MIMO systems, *Mathematics of Control, Signals, and Systems*, 18 (2006), 199-235.

A. Quadrat, A lattice approach to analysis and synthesis problems, *Mathematics of Control, Signals, and Systems*, 18 (2006), 147-186.

F. Chyzak, A. Quadrat, D. Robertz, Effective algorithms for parametrizing linear control systems over Ore algebras, *Applicable Algebra in Engineering, Communication and Computing*, 16 (2005), 319-376.

A. Quadrat, On a general structure of the stabilizing controllers based on stable range, *SIAM Journal on Control and Optimization*, 42 (2004), 2264-2285.

A. Quadrat, On a generalization of the Youla-Kucera parametrization. I. The fractional ideal approach to SISO systems, *Systems & Control Letters*, 50 (2003), 135-148.

A. Quadrat, The fractional representation approach to synthesis problems: An algebraic analysis viewpoint. I. (Weakly) doubly coprime factorizations, *SIAM Journal on Control and Optimization*, 42 (2003), 266-299.

A. Quadrat, The fractional representation approach to synthesis problems: An algebraic analysis viewpoint. II. Internal stabilization, *SIAM Journal on Control and Optimization*, 42 (2003), 300-320.

J.-F. Pommaret, A. Quadrat, Algebraic analysis of linear multidimensional control systems, I*MA Journal of Mathematical Control and Information*, 16 (1999), 275-297.