Global stabilization of discrete-time homogeneous systems |
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Authors: | H Hammouri S Benamor |
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Affiliation: | L.A.G.E.P. UPRES-A CNRS Q 5007 bât. 308G, Université Claude Bernard Lyon I et ESCPE-LYON 43, Bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France |
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Abstract: | The feedback stabilization of continuous time Δr-homogeneous systems has been studied by several authors, see for instance (Dayawansa and Martin, Proceedings of the 28th C.D.C., Tampa, Florida, December, 1989, Hermes, J. Differential Equations 92 (1991) 76–89, Hermes, Systems Control Lett. 24 (1995) 7–11, Kawski, Proceedings of the 27th C.D.C., Texas, 1988, Texas, Kawski, Control Theory and Advanced Technology, vol. 6, MITA Press, Tokyo, 1996, pp. 497–516, Sepulchre and Aeyels, Math. Control Signal Systems 9 (1996) 34–58). In (Kawski, Analysis of Controlled Dynamical Systems, Birkhauser, Basel, 1991, Kawski, Proceedings of IFAC NOLCOS, 1995), Kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations. In this note, we define the homogeneity of transition maps w.r.t. continuous dilations and we show how one can construct a global stabilizing feedback control for discrete-time homogeneous systems which are locally asymptotically stabilizable. |
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Keywords: | Discrete-time system Homogeneous system Feedback stabilization |
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