Model-Based Control Of Singularly Perturbed Networked Systems With Uncertain Nonlinear Disturbance

In this paper, the model-based networked control for singularly perturbed systems (SPSs) with uncertain nonlinear disturbance is investigated. The controlled plant is given by a singularly perturbed dynamical system with an uncertain nonlinear disturbance. The controller is designed based on a model system, which is taken as the nominal system of the controlled plant. The feedback signal is transmitted via a communication network. The uncertain disturbance of the SPSs of this paper does not satisfy the matching condition with a usual linear structure, but satisfies some certain Lipschitz condition. In the framework of the model-based networked control, we can't get an explicit expression of the slow and fast test matrices of the response (solution) because the targeted overall system is a class of singularly perturbed discontinuous (switch) dynamical systems with a Lipschitz nonlinear disturbance. Therefore, the useful two time-scale technique for the SPSs with a linear disturbance is no longer applicable for the system of this paper. To this end, we start directly from the theory of discontinuous dynamical system to solve this issue by using of the result which states that two discontinuous dynamical systems have the same type of stability if they have a stability preserving mapping between them. Based on this result, an appropriate stability preserving mapping is constructed between the overall discontinuous SPSs with a Lipschitz nonlinear disturbance and some certain two-dimensional linear singularly perturbed differential inclusion. Then, the stability the overall discontinuous SPSs with a Lipschitz nonlinear disturbance, which is difficult to solve, converted into the stability issue of the two-dimensional linear singularly perturbed differential inclusion. Three different signal transmission ways, a fixed sampling, time-varying sampling and the transmission with delay are studied, respectively. Finally, a numerical simulation is presented to illustrate the main results.