Decentralized Event-Triggered Control for Large-Scale Networked Fuzzy Systems

This paper addresses event-triggered data transmission in a class of large-scale networked nonlinear systems with transmission delays and nonlinear interconnections. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi-Sugeno model, and exchanges its information through a digital channel. We propose an event-triggering mechanism, which determines when the premise variables and system states should be transmitted to the controller. Our goal is to design a decentralized event-triggered state-feedback fuzzy controller, such that the resulting closed-loop fuzzy control system is asymptotically stable while the measured information is transmitted to the controller as little as possible. By using the input delay and perturbed system approaches, the closed-loop sampled-data fuzzy system with event-triggered control is first reformulated into a continuous-time system with time-varying delay and extra disturbance. Then, based on the new model, we introduce a Lyapunov-Krasovskii functional with virtue of Wirtinger's inequality, where not all of the Lyapunov matrices are required to be positive definite. The codesign result is derived to obtain simultaneously the controller gains, sampled period, network delay, and event-triggered parameter in terms of a set of linear matrix inequalities. Finally, two simulation examples are provided to validate the advantage of the proposed method.