Practical stochastic synchronisation of coupled harmonic oscillators subjected to heterogeneous noises and its applications to electrical systems

© The Institution of Engineering and Technology 2018. This study focuses on the practical stochastic synchronisation of coupled harmonic oscillators subjected to heterogeneous noises, where the dissipative and restorative couplings are no longer required in the connected network topologies. By employing the variational approach in combination with Lyapunov-like analysis, some simple yet generic practical synchronisation criteria are established in the sense of probability distribution and of mean square for coupled harmonic oscillator with directed network topology. Three main issues on stochastic synchronisation, including practical distribution synchronisation, stochastic distribution synchronisation, and practical mean square synchronisation, as well as their differences and relationships are fully addressed. The developed practical synchronisation criteria are then applied to a representative model of electrical systems which are composed of LC oscillators with linear time-invariant (LTI) resistors and inductors. Finally, numerical simulations are provided to show the effectiveness of the developed methods