Stability analysis of T–S fuzzy coupled oscillator systems influenced by stochastic disturbance

Coupled oscillator systems under the stochastic disturbance in practical have nonlinearity and uncertainty. To overcome the issue, the T–S fuzzy coupled oscillator system (TSFCOS) model is proposed in this paper, which provides an effective solution to coupled oscillator systems that are complex, uncertain and ill-defined. Subsequently, with the proposed nonlinear T–S fuzzy control, we give insight to the stability of the TSFCOSs with stochastic disturbance. Combined Lyapunov method and graph-theoretical technique, a systematic method to construct a global Lyapunov function for TSFCOSs is first provided, and then substantial stability criteria with the condition of the system topology property are obtained. Considering the application of our theoretical results in practical engineering, microgrids (the power networks) can be regarded as a kind of TSFCOSs with stochastic disturbance. With a numerical test of a six-generator seven-bus microgrid, the progressiveness and feasibility of our theoretical results are shown.