Event-Based Control for Networked T-S Fuzzy Systems via Auxiliary Random Series Approach

This paper presents an auxiliary random series approach to model the effect of network induced problems, such as data losses and transmission delay subject to event-based communication scheme for nonlinear continuous time systems. T-S fuzzy model is employed to describe the nonlinear systems. In order to save the bandwidth and energy, we introduce the event-triggered mechanism to reduce the number of data for transmission and computation. Thus, it is necessary to consider the influence of data losses, data disorder, and transmission delay since the transmitted data packets become more important. Consequently, it is very complicated to analyze the performance of such networked system and one of the most difficult part, in the authors' opinion, is to construct the mathematical model of closed-loop systems. In this paper, we present an auxiliary random series approach to describe the data transmitted in the system, and therefore, the closed-loop systems can be obtained. Associated with a tailor-made Lyapunov-Krasovskii functional, the stability analysis is processed and a fuzzy controller is designed. Asynchronous membership functions are considered to obtain more relaxed stability conditions. To clarify the effectiveness of the proposed method, a cart-damper-spring system is employed for simulation.