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Stabilization of homogeneous bilinear systems. (English) Zbl 0797.93039
Summary: We investigate the problem of stabilization of homogeneous bilinear systems. We show that if a bilinear system is locally asymptotically stabilizable by a state feedback law, then it becomes globally asymptotically stabilizable by some feedback law with the same upper bound.

MSC:
93D15 Stabilization of systems by feedback
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[1] Jurdjevic, V.; Quinn, H., Controllability and observability, Journal of differential equations, 12, (1978) · Zbl 0417.93012
[2] Gauthier, J.P.; Bornard, G., Stabilisation des systèmes non-linéaires, (), 307-324 · Zbl 0513.93045
[3] Artstein, Z., Stabilization with relaxed controls, Nonlinear anal. TMA, 7, 1163-1173, (1983) · Zbl 0525.93053
[4] Sonntag, E.D., A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization, Systems and control letters, 13, 2, 117-123, (1989) · Zbl 0684.93063
[5] Tsinias, Remarks on feedback stabilization of homogeneous systems, Control theory and advanced technology, 6, 4, 533-541, (1990)
[6] Rosier, L., Homogeneous Lyapunov function for homogeneous continuous vector field, System and control letters, 19, 467-473, (1992) · Zbl 0762.34032
[7] Masséra, J.L., Contribution to stability theory, J. of differential equations, 64, 1, 182-206, (1956) · Zbl 0070.31003
[8] Hermes, H., Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, Lecture notes in applied and pure mathematics, 249-260, (1991), No. 127
[9] Outbib, R.; Sallet, G., Stabilizability of the angular velocity of a rigid body revisited, Systems and control letters, 18, 2, 93-98, (1992) · Zbl 0743.93082
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