Stabilization of polynomial systems in ℝ³ via homogeneous feedback

• Autorzy: Jerbi Hamadi , Kharrat Thouraya , Mabrouk Fehmi

Identyfikatory

DOI

10.1515/jaa-2021-2080

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

Słowa kluczowe

EN

homogeneous system; polynomial systems; stabilization; homogeneous feedback; periodic orbits

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 189--197
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Jerbi Hamadi

• Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Sfax, Tunisia

autor

Kharrat Thouraya

• Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Sfax, Tunisia

• https://orcid.org/0000-0002-5171-3938

autor

Mabrouk Fehmi

• Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Sfax, Tunisia

Bibliografia

• [1] C. Coleman, Asymptotic stability in 3-space, in: Contributions to the Theory of Nonlinear Oscillations. Vol. V, Princeton University, Princeton (1960), 257-268.
• [2] W. P. Dayawansa, C. F. Martin and S. Samelson, Asymptotic stabilization of a generic class of three-dimensional homogeneous quadratic systems, Systems Control Lett. 24 (1995), no. 2, 115-123.
• [3] W. Hahn, Stability of Motion, Grundlehren Math. Wiss. 138, Springer, New York, 1967.
• [4] H. Jerbi and T. Kharrat, Stabilization of homogeneous polynomial systems in the plane, Systems Control Lett. 48 (2003), 87-99.
• [5] H. Jerbi, T. Kharrat and F. Omri, Global stabilization of a class of bilinear systems in ℝ³, Mediterr. J. Math. 13 (2016), no. 5, 2507-2524.
• [6] H. Jerbi, T. Kharrat and K. Sioud, Stabilization of homogeneous polynomial systems in the plane, Kybernetika (Prague) 52 (2016), no. 1, 131-152.
• [7] M. Kawski, Homogeneous stabilizing feedback laws, Control Theory Adv. Tech. 6 (1990), no. 4, 497-516.
• [8] J. L. Massera, Contributions to stability theory, Ann. of Math. (2) 64 (1956), 182-206.
• [9] L. Menini and A. Tornambè, Stabilization of polynomial nonlinear systems by algebraic geometry techniques, IEEE Trans. Automat. Control 60 (2015), no. 9, 2482-2487.
• [10] M. Oumoun and J. C. Vivalda, On the global stabilization of a class of bilinear systems in 3-space, European J. Control 2 (1996), 193-200.
• [11] L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field, Systems Control Lett. 19 (1992), 467-473.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).