Synchronization of chaotic oscillators using partial state space linear control

The idea of synchronization of chaotic oscillators traces its origin to pioneering work by T. L. Carroll and L. M. Pecora in the late 1980s. Numerous implementations reported over the last three decades either require all state variables of a master oscillator to generate a locking signal to entrain the slave oscillators, or use a subset of the state variables, albeit with nonlinear transfer function. We present a novel methodology in which locking signal is generated as i) a linear combination of ii) a partial subset of state variables of the oscillators. The unused state variables can be exploited for applications in cryptography. A generalized algorithm for controller design is presented, and the efficacy of this algorithm is proved by analyzing the piece-wise oscillator as multi-mode linear system. Root-locus method is used to compute feedback gain. Simplicity of the control system makes it possible to reliably realize all-analog, all-digital, or mixed-signal implementations for electronic oscillators, with low power and cost overheads. The methodology is validated through numerical simulations and experiments using op-amp based electronic circuits.