Stability and Stabilization of Fuzzy Event-Triggered Control for Positive Nonlinear Systems

This paper is concerned with the stabilization and event-triggered control for positive nonlinear systems in terms of Takagi–Sugeno (T–S) fuzzy models. By employing the unique positivity of positive systems, a new event-triggered mechanism is introduced to select necessary signals so that the communication resources can be saved effectively while guaranteeing the system performance. It is different from the traditional event-triggered mechanism that is designed in the quadratic form for general systems, the one adopted in this paper is in linear form which is beneficial to facilitate the stability analysis in terms of a linear copositive Lyapunov function. However, the tricky non-convex problem makes controller design extremely challenging. For handling this issue, the matrix decomposition technique plays a very important part in designing the feedback control law. Furthermore, improving the relaxation of the analysis results is another considerably vital but challenging issue. To break through this difficulty, an asynchronous premise re-construct method is presented to extract the information of membership functions (MFs), which is conducive to obtaining more relaxed stability and positivity analysis. Finally, the validity of this control strategy is illustrated by simulation examples.