Stability analysis of T-S fuzzy-model-based coupled control systems with nonlinear T-S fuzzy control and its application

Takagi-Sugeno (T-S) fuzzy model offers a general and systematic framework to represent a nonlinear plant and provides an effective platform to facilitate stability analysis and control synthesis. This paper is concerned with the stability of the equilibrium point of a class of T-S fuzzy-model-based coupled control systems (TSFCCSs). Combined the Lyapunov method and graph theory, a systematic method to construct a global Lyapunov function for TSFCCSs is proposed, and then the substantial criteria of global stability at the equilibrium point with the condition of the system topology property are obtained. The theoretical results are suitable for the microgrid which is an application of the coupled control system. The significance of the presented results is that the global asymptotic stability of the microgrid can be achieved at the equilibrium point owing to the proposed secondary nonlinear T-S fuzzy control. Finally, one numerical simulation of a microgrid with six-generator seven-bus topology is presented to illustrate the progressiveness and feasibility of our results.