# Control Theory

Our work in control theory is a recent activity and it is done in collaboration with some groups of specialists. We started with a well-known problem, the study of the stability of differential delay systems and multidimensional systems with an important observation: with a correct modelization, some recent algebraic methods, derived from our work in algorithmic geometry and shared with applications in robotics, now allow some previously impossible computations and lead to a better understanding of the problems to be solved.

• G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat, and F. Rouillier, “Explicit H$\infty$ controllers for 4th order single-input single-output systems with parameters and their applications to the two mass-spring system with damping,” in IFAC 2017 Workshop Congress , Toulouse, France, 2017.
[Bibtex]
@inproceedings{rance:hal-01667368,
TITLE = {{Explicit H$\infty$ controllers for 4th order single-input single-output systems with parameters and their applications to the two mass-spring system with damping}},
AUTHOR = {Rance, Guillaume and Bouzidi, Yacine and Quadrat, Alban and Quadrat, Arnaud and Rouillier, Fabrice},
URL = {https://hal.inria.fr/hal-01667368},
BOOKTITLE = {{ IFAC 2017 Workshop Congress }},
YEAR = {2017},
MONTH = Jul,
HAL_ID = {hal-01667368},
HAL_VERSION = {v1},
}
• Y. Bouzidi, A. Quadrat, and F. Rouillier, Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems, 2017.
[Bibtex]
@unpublished{bouzidi:hal-01571230,
TITLE = {{Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems}},
AUTHOR = {Bouzidi, Yacine and Quadrat, Alban and Rouillier, Fabrice},
URL = {https://hal.inria.fr/hal-01571230},
TYPE = {Research Report},
NUMBER = {RR-9085},
PAGES = {31},
INSTITUTION = {{INRIA Lille - Nord Europe ; INRIA Paris}},
YEAR = {2017},
MONTH = Aug,
KEYWORDS = {Multidimensional systems ; structural stability ; stability analysis ; computer algebra ; polynomial equations ; Syst{\e}mes multidimensionnels, stabilit{\'e} structurelle, analyse de stabilit{\'e}, calcul formel, {\'e}quations polynomiales},
PDF = {https://hal.inria.fr/hal-01571230/file/RR-9085.pdf},
HAL_ID = {hal-01571230},
HAL_VERSION = {v1},
NOTE={To appear in Multidimensional Systems and Signal Processing, \url{https://link.springer.com/article/10.1007/s11045-018-0596-y}},
}
• Y. Bouzidi and F. Rouillier, “Certified Algorithms for proving the structural stability of two dimensional systems possibly with parameters,” in MNTS 2016 – 22nd International Symposium on Mathematical Theory of Networks and Systems, Minneapolis, United States, 2016.
[Bibtex]
@inproceedings{bouzidi:hal-01366202,
TITLE = {{Certified Algorithms for proving the structural stability of two dimensional systems possibly with parameters}},
AUTHOR = {Bouzidi, Yacine and Rouillier, Fabrice},
URL = {https://hal.inria.fr/hal-01366202},
BOOKTITLE = {{MNTS 2016 - 22nd International Symposium on Mathematical Theory of Networks and Systems}},
}`