An observer looks at synchronization

In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory,.

[1]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[2]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[3]  and Charles K. Taft Reswick,et al.  Introduction to Dynamic Systems , 1967 .

[4]  J. Willems,et al.  Stability theory of dynamical systems , 1970 .

[5]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[6]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[7]  Thomas Kailath,et al.  Linear Systems , 1980 .

[8]  D. Aeyels.  GENERIC OBSERVABILITY OF DIFFERENTIABLE SYSTEMS , 1981 .

[9]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[10]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[11]  D. Aeyels.  On the number of samples necessary to achieve observability , 1981 .

[12]  Verne C. Fryklund,et al.  What systems analysis? , 1981, Nature.

[13]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[14]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[15]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[16]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

[17]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[18]  E. Ott,et al.  Controlling Chaotic Dynamical Systems , 1991, 1991 American Control Conference.

[19]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[20]  He,et al.  Analysis and synthesis of synchronous periodic and chaotic systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[21]  Tambe,et al.  Driving systems with chaotic signals. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[22]  J. Gauthier,et al.  Global time-varying linearization up to output injection , 1992 .

[23]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[24]  Alan V. Oppenheim,et al.  ROBUSTNESS AND SIGNAL RECOVERY IN A SYNCHRONIZED CHAOTIC SYSTEM , 1993 .

[25]  Maciej Ogorzalek,et al.  Taming chaos. I. Synchronization , 1993 .

[26]  T. Carroll,et al.  Synchronizing nonautonomous chaotic circuits , 1993 .

[27]  A. Tesi,et al.  A frequency approach for analyzing and controlling chaos in nonlinear circuits , 1993 .

[28]  H. Nijmeijer,et al.  On output linearization of observable dynamics , 1993 .

[29]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

[30]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[31]  Chai Wah Wu,et al.  A Simple Way to Synchronize Chaotic Systems with Applications to , 1993 .

[32]  Leon O. Chua,et al.  EXPERIMENTAL SYNCHRONIZATION OF CHAOS USING CONTINUOUS CONTROL , 1994 .

[33]  A. Tesi,et al.  ON SYSTEM DECOMPOSITION FOR SYNCHRONIZING CHAOS , 1994 .

[34]  Ott,et al.  Enhancing synchronism of chaotic systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  L. Chua,et al.  A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS , 1994 .

[36]  Carroll,et al.  Transforming signals with chaotic synchronization. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  Morgül,et al.  Observer based synchronization of chaotic systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  G. Besancon.  Contributions à l'étude et à l'observation des systèmes non linéaires avec recours au calcul formel , 1996 .

[39]  Peng,et al.  Synchronizing hyperchaos with a scalar transmitted signal. , 1996, Physical review letters.

[40]  Y. Lai,et al.  Controlling chaotic dynamical systems , 1997 .

[41]  A.L. Fradkov,et al.  Self-synchronization and controlled synchronization , 1997, 1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No.97TH8329).