Stability Analysis and Event-Triggered Control for IT2 Discrete-Time Positive Polynomial Fuzzy Networked Control Systems With Time Delay

This paper investigates the stability analysis and event-triggered controller design of interval type-2 (IT2) discrete-time positive polynomial fuzzy networked control (DPPFNC) systems with time delay subject to asynchronous premises. The reasonable design of the IT2 polynomial fuzzy event-triggered controller guarantees the closed-loop system's positivity and stability, reduces energy consumption and efficiently utilizes the communication bandwidth. Furthermore, for DPPFNC systems with time delay, obtaining more relaxed stability conditions and lower network communication frequency is quite challenging, even for the current advanced theory. Meanwhile, to strengthen the practicality of the control strategy, the asynchronous constraints of premise variables due to the introduction of the network are considered. Aiming at the above problems, a polynomial fuzzy event-triggered control strategy is proposed based on the stability analysis of IT2 membership-function-dependent (IT2-MFD) and imperfect premise matching (IPM). First, the IT2 polynomial fuzzy model, which employs IT2-MFs to capture parameter uncertainty, depicts the event-triggered positive nonlinear dynamics. Second, an IT2 polynomial fuzzy event-triggered controller is designed by introducing the 1-norm event-triggered control (ETC) strategy. Then, by optimizing the approximation error between the original and the approximate membership function, a genetic algorithm (GA) is employed to relax the stability criteria. Finally, numerical and practical examples illustrate the viability of the suggested design.