On Model-Based Networked Control Of Singularly Perturbed Systems With Time-Varying Transmission Times

In this paper, the state feedback control of the linear singularly perturbed plant is discussed, where the sensor and the controller/actuator are connected via a network and the transmission frequency is time-varying. Because of the existence of the small parameter e, the plant system has two-time scales. Taking advantages of the de-coupled form of the linear singularly perturbed systems, the analysis of matrix perturbation and Laplace transformation, the existence of the bound of e is shown to guarantee stability of the whole closed-loop singularly perturbed system.We have done two problems as follows:1. Under the reasonable conditions, that is, the original plant is standard singularly perturbed system and the model plant is controllable, the approximate slow and fast subsystems on each sampling interval are given which base on the whole system, we obtain the sufficient conditions for the original overall closed-loop system is exponential stability with time-varying transmission times .2. The sampling times are driven by a stochastic process with identically independently distributed and Markov-chain driven transmission times are introduced. Sufficient conditions for the whole system is probability-1 stability and mean-square stability are derived by using the statistical knowledge.