Graph theory-based approach for stability analysis of stochastic coupled oscillators system by energy-based synchronization control

This paper investigates the stability of stochastic coupled oscillators systems (SCOSs) by the mechanical energy of the oscillators. Assembling mechanical energy from the single oscillator system with the help of graph theory, a systematic method to construct a global Lyapunov function for SCOSs is provided. And then two types of stability criteria with the condition of the system topology property are presented. The significance of the presented results is that the stochastic global asymptotical stability of SCOSs can be achieved at equilibrium via an energy-based synchronization control law. Subsequently, the theoretical results are applied to parallel multi-inverter microgrid (a power network) with stochastic disturbance. And a numerical example about microgrid with six-generator seven-bus topology is given to verify the progressiveness and effectiveness of the proposed scheme through Matlab/Simulink simulation.