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Original Articles

Feedback stabilization of nonlinear discrete-time systems

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Pages 579-596 | Received 05 Apr 1995, Published online: 29 Mar 2007

References

  • Abed , E. H. and Fu , J.-H. 1986 . Local feedback stabilization and bifurcation control. I. Hopf bifurcation . Systems Control Lett. , 7 : 11 – 17 .
  • Abed , E. H. and Fu , J.-H. 1987 . Local feedback stabilization and bifurcation control. II. Stationary bifurcation . Systems Control Lett. , 8 : 467 – 473 .
  • Abed , E. H. , Wang , H. O. and Chen , R. C. 1992 . Stabilization of period doubling bifurcations and implications for control of chaos . Proc. 31th Conference on Decision and Control , 8 : 2119 – 2124 . Tucson, Arizona, December 1992, IEEE
  • Aeyels , D. 1985 . Stabilization of a class of nonlinear systems by a smooth feedback control . Systems Control Lett. , 5 : 289 – 294 .
  • Andronov , A. A. , Leontovich , E. A. , Gordon , I. I. and Maier , A. G. 1967 . Theory of Bifurcation of Dynamical Systems in the Plane Moscow, Russian
  • Aulbach , B. Springer 1984 . “ Continuous and Discrete Dynamics near Manifolds of Equilibria ” . In Lecture Notes in Mathematics Vol. 1058 , Springer , Berlin
  • Bacciotti , A. 1992 . Local Stabilizability of Nonlinear Control Systems , Singapore : World Scientific .
  • Byrnes , C. I. and Lin , W. 1994 . Losslessness, feedback eqivalence and the global stabilization of discrete-time systems . IEEE Trans. Automat. Control , 39 : 83 – 98 .
  • Byrnes , C. I. and Lin , W. 1994 . Global stabilization of discrete-time systems: a passive system approach . Proc. SIAM Conf. on Control and its Applications, Minneapolis , 39
  • Byrnes , C. I. , Lin , W. and Ghosh , B. K. 1993 . Stabilization of discrete-time nonlinear systems by smooth state feedback . Systems Control Lett. , 21 : 255 – 263 .
  • Carr , J. 1981 . Applications of Centre Manifold Theory , New York : Springer .
  • Dsesow , I. , Leonov , G. and Reitmann , V. 1986 . Stabilisierung diskreter Systeme durch harmonische äuβere Wirkung . Wiss. Z. Tech. Univ. Dresden , 35 ( 4 ) : 11 – 13 .
  • Fomin , V. N. 1991 . Discrete Linear Control Systems , Dordrecht : Kluwer .
  • Guckenheimer , J. and Holmes , P. 1983 . Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , New York : Springer .
  • Hahn , W. 1967 . Stability of Motion , Berlin : Springer .
  • Hammer , J. 1989 . State feedback for nonlinear control systems . Int. J. Control , 50 : 1961 – 1980 .
  • Hirsch , M. , Pugh , C. and Shub , M. 1977 . “ Invariant Manifolds ” . In Lecture Notes in Mathematics , Vol. 583 , Berlin : Springer .
  • Iooss , G. 1979 . Bifurcation of Maps and Applications , Amsterdam : North-Holland .
  • Kalman , R. E. , Falb , P. L. and Arbib , M. A. 1969 . Topics in Mathematical System Theory , New York : McGraw-Hill .
  • Kirchgraber , U. and Palmer , K. J. 1990 . “ Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearzation ” . In Pitman Research Notes in Mathematics Series , Vol. 233 , Harlow : Longman .
  • Krut'ko , P. D. 1984 . Synthesis of discrete controls from Lyapunov functions . Eng. Cybern , 22 : 95 – 102 . translation from Izv. Akad. Nauk SSSR. Tekh. Kibern. 1984, no. 2, 148-156
  • Lasalle , J. P. 1986 . The Stability and Control of Discrete Processes , New York : Springer .
  • Lee , K. K. and Araposthatis , A. 1988 . Remark on smooth feedback stabilization of nonlinear systems . Systems Control Lett. , 10 : 41 – 44 .
  • Lun'kov , V. A. 1989 . On preservation of stabilizability in case of difference approximation of linear systems (Russian) . Nonlinear Oscillations and Control Theory, Interuniv. Collect. Sci. Works. Izhevsk. , 10 : 75 – 85 .
  • Marsden , J. E. and McCracken , M. 1976 . The Hopf Bifurcation and Its Applications , New York : Springer .
  • Müller , W. and Schneider , K. R. 1976 . Feedback stabilization of nonlinear discrete-time systems. WIAS-Preprint No. 85 (1994). www.wias-berlin.de/WIAS_pupl_preprints_nr.85.ps ,
  • Pliss , V. A. 1964 . The principle of reduction in the theory of stability of motion (Russian) . Izv. Akad. Nauk SSSR. Ser. mat. , 30 : 911 – 924 .
  • Ruelle , D. 1989 . Elements of Differentiable Dynamics and Bifurcation Theory , San Diego : Academic Press .
  • Schneider , K. R. 1980 . Andronov-Hopf-Bifurkation im Falle stetiger Parameterabhängigkeit . Z. Angrew. Math. Mech. , 60 : 19 – 24 .
  • Sontag , E. D. 1990 . Mathematical Control Theory. Deterministic Finite Dimensional Systems , New York : Springer .
  • Tsinias , J. 1989 . Stabilizability of discrete-time nonlinear systems . IMAJ Control Inform , 6 : 135 – 150 .
  • Tsinias , J. and Kalouptsidis , N. 1990 . Output feedback stabilization of discrete-time control systems . IMAJ. Control Inform , 7 : 257 – 268 .

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