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A manifold-like characterization of asymptotic stabilizability of homogeneous systems. (English) Zbl 0987.93060
Summary: We present a version of Artstein’s theorem for homogeneous systems, and we drive sufficient manifold-like conditions for the stabilization of single-input homogeneous systems by means of a homogeneous feedback law.

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
Full Text: DOI
[1] Andriano, V., Global feedback stabilization of the angular velocity of a symmetric rigid body, Systems control lett., 10, 251-256, (1988)
[2] Artstein, Z., Stabilization with relaxed controls, Nonlinear anal. TMA, 7, 1163-1173, (1983) · Zbl 0525.93053
[3] Barbashin, E.A., Introduction to the theory of stability, (1970), Wolters-Noordhoff Groningen · Zbl 0198.19703
[4] Grune, L., Homogeneous state feedback stabilization of homogeneous control systems, SIAM J. control optim., 38, 1288-1314, (2000) · Zbl 0958.93077
[5] Lefschetz, S., Stability of nonlinear control systems, (1965), Academic Press New York · Zbl 0136.08801
[6] Sontag, E.D., A “universal” construction of Artstein’s theorem on nonlinear stabilization, Systems control lett., 13, 2, 117-123, (1989) · Zbl 0684.93063
[7] Tsinias, J., Stabilization of affine in control nonlinear systems, Nonlinear analysis TMA, 12, 1283-1296, (1988) · Zbl 0662.93055
[8] Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Math. control signals systems, 2, 343-357, (1989) · Zbl 0688.93048
[9] Utkin, V.I., Variable structure systems with sliding mode: a survey, IEEE trans. automat. control AC, 22, 212-222, (1977) · Zbl 0382.93036
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