Fuzzy-model-based output feedback control for nonlinear singularly perturbed systems with time-scale-dependent decode-and-forward relay strategy

This paper focuses on the output feedback control problem for fuzzy singularly perturbed systems (SPSs) with packet dropouts. Three Bernoulli random variables are introduced to describe the packet loss behaviors of different network channels between sensors and controllers. A time-scale-dependent decode-and-forward (TSDDaF) relay scheme is proposed to improve the remote transmission of the fuzzy SPSs, in which the slow and fast measurement signal can be decoded and reconstructed separately according to the different time scales. The key results of this article can be summarized in two aspects: (1) Firstly, by exploiting the received slow and fast signals from both the relays and sensors via different channels, a TSDDaF relay-based composite fuzzy output feedback controller is designed, under which the control performance of fuzzy SPSs can be effectively improved. (2) Secondly, by establishing a singular perturbation parameter-dependent Lyapunov functional, the sufficient conditions for exponentially ultimately boundedness (EUB) in mean square sense can be obtained and the numerical stiffness problem can be avoided. The feasibility of our approach is illustrated through a flexible joint inverted pendulum example.