Projective synchronization via a linear observer: Application to time-delay, continuous-time and discrete-time systems

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 (FDEs), continuous-time systems described by ordinary differential equations (ODEs) and discrete-time systems described by difference equations ( DEs). 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.