Modeling and stability of long random delay networked control systems

The work of this paper is the first step of the Networked Control Systems Project. In this paper, modeling and stability of the long random delay networked control systems are discussed. The objective is to present a model for such systems, and discuss the systems´ stability under such a model. First, we employ the multirate sampling method together with the augmented state matrix method to model the long random delay networked control systems. Secondly, by formulating the modeled systems as discrete-time switched systems, the long random delay networked control systems´ stability can be reduced to the corresponding problems of the discrete-time switched systems. By applying the available results in the literature for the discrete-time switched systems, we present a theorem about the sufficient conditions of the systems´ dwell time stability and discuss how to select the proper N so as to stabilize the systems considering rigorous stability and get a good system performance as well.