Projective synchronization via a linear observer: application to time-delay, continuous-time and discrete-time systems. (English) Zbl 1139.93348

Grassi, Giuseppe; Miller, Damon A.

Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 4, 1337-1342 (2007).

Summary: This letter presents a general approach to projective synchronization that features a linear observer with an ability to arbitrarily scale a drive system attractor. The technique can be applied to wide classes of chaotic and hyperchaotic systems, namely time-delay systems described by functional differential equations, continuous-time systems described by ordinary differential equations and discrete-time systems described by difference equations. Theoretical and simulation results demonstrate that a linear observer can duplicate chaotic system states in any desired scale using only a scalar synchronizing signal. The proposed approach is readily implemented in hardware.

MSC:

93D15	Stabilization of systems by feedback
34K20	Stability theory of functional-differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C23	Control/observation systems governed by functional-differential equations
93B07	Observability

Keywords:

chaos synchronization; attractor scaling; linear observer

References:

[1]	DOI: 10.1016/0375-9601(90)90283-T
[2]	DOI: 10.1016/j.physleta.2003.09.024 · Zbl 1098.37512
[3]	DOI: 10.1109/81.633891
[4]	DOI: 10.1049/el:19980099
[5]	DOI: 10.1109/82.755422 · Zbl 1159.94361
[6]	DOI: 10.1109/81.989174
[7]	Lu H., IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 45 pp 178–
[8]	DOI: 10.1103/PhysRevLett.82.3042
[9]	DOI: 10.1109/81.915393
[10]	DOI: 10.1016/0375-9601(95)00208-K
[11]	DOI: 10.1049/el:19960630
[12]	DOI: 10.1016/j.physleta.2004.10.072 · Zbl 1123.37326
[13]	DOI: 10.1016/j.chaos.2004.09.117 · Zbl 1122.93311
[14]	DOI: 10.1103/PhysRevE.63.027201
[15]	DOI: 10.1103/PhysRevE.66.046218