Reachable set bounding of output-feedback control for discrete-time large-scale IT-2 fuzzy descriptor systems using distributed event-based broadcasts

Abstract

This paper studies the distributed event-based broadcasting of output-feedback control for discrete-time large-scale fuzzy descriptor systems subject to reachable set bounding. First, each nonlinear subsystem is represented by the interval type-2 fuzzy model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into the linear one. Then, we introduce an output-feedback fuzzy controller with distributed event-based broadcasting, where all subsystems communicate with each other via a distributed network, and each subsystem broadcasts its decision-making of transmission based on a prescribed event. Two event-based mechanisms (EBMs) are respectively proposed to examine when the system output and fuzzy premise variable should be transmitted to the controller. Moreover, by further employing a descriptor redundancy representation, combined with reachable set analysis method, it will be shown that the proposed fuzzy controller guarantees that the estimation error is bounded within the ellipsoidal boundary while communication data are transmitted to the controller as little as possible, and sufficient condition for designing the desired controller is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study is given to show the effectiveness of the proposed method.