zbMATH — the first resource for mathematics

Only a level set of a control Lyapunov function for homogeneous systems. (English) Zbl 1249.93147
Summary: In this paper, we generalize Artstein’s theorem and we derive sufficient conditions for stabilization of single-input homogeneous systems by means of an homogeneous feedback law and we treat an application for a bilinear system.

93D15 Stabilization of systems by feedback
Full Text: Link EuDML
[1] Artstein Z.: Stabilization with relaxed controls. Nonlinear. Anal. 7 (1983), 1163-1173 · Zbl 0525.93053 · doi:10.1016/0362-546X(83)90049-4
[2] Faubourg L., Pomet J. P.: Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems. ESAIM: Control, Optimization and Calculus of Variations 5 (2000), 293-311 · Zbl 0959.93046 · doi:10.1051/cocv:2000112 · www.edpsciences.org · eudml:90572
[3] Goodman R. W.: Nilpotent Lie Groups: Structure and Applications to Analysis. (Lecture Notes in Mathematics 562.) Springer-Verlag, Berlin 1976 · Zbl 0347.22001
[4] Hermes H.: Nilpotent and high-order approximations of vector field systems. SIAM Rev. 33 (1991), 238-264 · Zbl 0733.93062 · doi:10.1137/1033050
[5] Jerbi H.: A manifold-like characterization of asymptotic stabilizability of homogeneous systems. Systems Control Lett. 45 (2002), 173-178 · Zbl 0987.93060 · doi:10.1016/S0167-6911(01)00172-4
[6] Kawski M.: Homogeneous stabilizing feedback laws. Control Theory and Advanced Technology 6 (1990), 497-516
[7] Closkey R. Mac, Murray M.: Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans. Automat. Control 42 (1997), 614-628 · Zbl 0882.93066 · doi:10.1109/9.580865
[8] Closkey R. Mac, Morin P.: Time-varying homogeneous feedback: design tools for exponential stabilization of systems with drift. Internat. J. Control 71 (1998), 837-869 · Zbl 0979.93088 · doi:10.1080/002071798221605
[9] Sontag E. D.: A “universal” construction of Artstein’s Theorem on nonlinear stabilization. Systems Control Lett. 13 (1989) · Zbl 0684.93063 · doi:10.1016/0167-6911(89)90028-5
[10] Tsinias J.: Stabilization of affine in control nonlinear systems. Nonlinear Anal. 12 (1988), 1238-1296 · Zbl 0662.93055 · doi:10.1016/0362-546X(88)90060-0
[11] Tsinias J.: Sufficient Lyapunov like conditions for stabilization. Math. Control Signals Systems 2 (1989), 343-357 · Zbl 0688.93048 · doi:10.1007/BF02551276
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.