Event-triggered Stabilization of Linear Time-delay Systems by Static Output Feedback Control
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Event-triggered Stabilization of Linear Time-delay Systems by Static Output Feedback Control Xiaoli Wang, Peng Xiang, Wenfeng Hu*, and Tingwen Huang Abstract: In this paper, we study the stabilization problem for a class of linear systems with a time-varying state delay. An event-triggered static output feedback controller is proposed, such that the sampling frequency and the update time of the controller are both lowered. First, we present a novel event-triggering mechanism depending not only on the output but also on an exponential term, with which less sampling is required and Zeno behavior can be excluded at the same time. Some sufficient conditions are then obtained, under which an exponential convergence can be achieved by means of the comparison principle approach. It is further shown that the parameters design can be easily given if the case reduces to the state feedback control. Moreover, two examples are presented to show the effectiveness of the results. Keywords: Event-triggered control, stabilization problem, static output feedback, time-varying delay.
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INTRODUCTION
As one fundamental issue, stabilization problem has been extensively studied for both linear and nonlinear systems. Many control problems, including the networked control problem and the state estimation problem, can be eventually converted into the stabilization problems (see [1, 2]). According to the information available for feedback control, the controller can be divided into state feedback and output feedback (see [3–7]). In particular, compared with the state feedback controller, the output feedback controller is more practical, because the system state may not be measurable in many scenarios. From a viewpoint of application, the static output feedback controller is easier for implementation, in contrast with the observer-based output feedback controller [8]. On the other hand, in practice, the time delay is unavoidable when the remote control systems through the Internet are distant from each other in the remote locations, which often leads to instability, oscillation, or other poor performance [9, 10]. In particular, compared with other types of time delays, the state delays are more general and inevitable. Recently, many attentions have been devoted to the stability analysis of the systems with time-varying delays, see [11–13] and the references therein.
In the implementation of the controllers, the information used is usually sampled periodically, which may cause the huge waste of energy. As an alternative method, the event-triggered control strategy can be used to lower the sampling frequency, which is quite important in a resource-limited environment [14]. Hence, the eventtriggered control has received considerable attention in recent years and a lot of research results have been reported, such as [15–17, 19–21]. However, it is worth mentioning that the developed controllers in the aforementioned literatures are state dependent, and few event-triggered controlle
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