A New Model for Time-delay Systems with Application to Network Based Control

Abstract: This paper proposes a new model for time-delay systems, which contains multiple successive delay components in the state and has important applications in remote control and network based control. New results on stability and H ∞ performance are obtained for systems with two successive delay components. The second part of this paper applies the proposed new model to network based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modelled as a time-delay system with two successive delay components in the state and, the problem of network based H ∞ control is solved accordingly. Key Words: Networked control, sampled-data systems, time-delay systems Motivation and New Model Time-delay systems, also called systems with aftereffect, equations with deviating argument or differentialdifference equations, have kept being an active research area for the last few decades. The main reason is that many processes include after-effect phenomena in their inner dynamics, and engineers require models to behave more like real processes due to the ever-increasing expectations of dynamic performance. There is a great number of research results concerning time-delay systems scattered in the literature (see, where d(t) is a time delay in the state x(t), which is often assumed to be either constant, or time-varying satisfying certain conditions, e.g., Almost all the reported results on time-delay systems are based on this basic mathematical model. It is noted that in IEEE Catalog Number: 06EX1310 This work was supported by an Alberta Ingenuity Fellowship, a Killam Memorial Postdoctoral Fellowship, and NSERC, Canada. This work was also partially supported by the Program for New Century Excellent Talents in University, and RGC Grant HKU 7028/04P. this model, the time delay in the state variable x(t) is assumed to appear in a single and simple form. Sometimes in practical situations, however, signals transmitted from one point to another may experience a few segments of networks, which can possibly induce successive delays with different properties due to variable network transmission conditions. Let us consider, for example, a state-feedback remote control problem. Suppose the physical plant is given byẋ(t) = Ax(t) + Bu(t), and suppose the measurement of x(t) travels through s segments of transmission media, each of which will cause some delay with different properties, denoted as d i (t), i = 1,...,s. In this case, the closed-loop system with state-feedback gain K is given byẋ and a natural assumption on the time delay d i (t) can be given by It can be seen that there are s successive delay components appearing in the state x(t). Since the properties of these delay components may not be identical due to the transmission conditions, it is not reasonable to combine them together. System 5