IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 5, NO. 6, NOVEMBER 2018 1089 Stabilization of Networked Control Systems Using a Mixed-Mode Based Switched Delay System Method Qing-Kui Li, Member, IEEE, Xiaoli Li, Jiuhe Wang, and Shengli Du Abstract—The phenomenon of mixed-mode is one of the most important characteristics of switched delay systems. If a networked control system (NCS) with network induced delays and packet dropouts (NIDs & PDs) is recast as a switched delay system, it is imperative to consider the effects of mixed-modes in the stability analysis for an NCS. In this paper, with the help of the interpolatory quadrature formula and the average dwell time method, stabilization of NCSs using a mixed-mode based switched delay system method is investigated based on a novel constructed Lyapunov-Krasovskii functional. With the Finsler’s lemma, new exponential stabilizability conditions with less conservativeness are given for the NCS. Finally, an illustrative example is provided to verify the effectiveness of the developed results. Index Terms—Interpolatory quadrature formula, mixed-mode, networked control system(NCS), switched delay system. I. I NTRODUCTION W ITH the rapid advancements of network technology, in a number of control engineering applications, sensors and actuators connect with a remote controller over a multipur- pose networks, allowing the networks to exchange information among distributed spatial system components. Such systems are well known as networked control system (NCSs) and have gained special interests due to their attractive features such as simple installation and maintenance, increased system flexibility, higher system testability and resource utilization, lower cost, and reduced weight and power [1]−[8]. Typical examples can be seen in a wide range of areas including industrial automation, satellite clusters, traffic control, and mobile robots [9]−[11]. Consequently, in the past decades, research on NCSs has attracted considerable attentions in control and network community, e.g., [12]−[20]. Despite the advantages of NCSs, the use of a shared network result in communication constrains due to the inherent limitation of Manuscript received April 13, 2018; accepted June 15, 2018. This work was supported by the National Natural Science Foundation of China (61573230, 61473034, 51777012), Beijing Nova Programme Interdisciplinary Coopera- tion Project (Z161100004916041), and in part by the Project of Promoting Universities’ Connotation Development for the Scientific Research Level Improvement of Beijing Institution Science and Technology University. Rec- ommended by Associate Editor Guoping Liu. (Corresponding author: Qing- Kui Li.) Citation: Q. K. Li, X. L. Li, J. H. Wang, and S. L. Du, “Stabilization of networked control systems using a mixed-mode based switched delay system method,” IEEE/CAA J. of Autom. Sinica, vol. 5, no. 6, pp. 1089−1098, Nov. 2018. Q. K. Li and J. H. Wang are with the School of Automation, Beijing Information Science and Technology University, Beijing 100192, China (e- mail: sdlqk01@126.com; wjhhrwm@163.com). X. L. Li and S. L. Du are with the Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China (e-mail: lixiaolib- jut@bjut.edu.cn; hoest100@126.com). Digital Object Identifier 10.1109/JAS.2018.7511228 network bandwidth. It is well recognized that network induced delays and packet dropouts (NIDs & PDs) are two important constrains which are the potential causes of performance deterioration or instability of the NCSs [21]. How NIDs & PDs affect the stability and performance of NCSs has thus become an important issue. Several methodologies have been devel- oped for modeling, analyzing and synthezing for NCSs in the presence of NIDs & PDs. Some important categories are mentioned for examples as follows: 1) Time delay system methodology models packet dropouts as a kind of delays, which are lumped with network induced delays in the system. Then, the NCS is modeled as a time delay system with mixed delays [22], [23]. 2) Stochastic system method holds the property of an NCS that intermittent packet dropouts and network induced delays are random, and is viewed as an important strategy to handle random phenomenon in NCS. One of the stochastic methods uses a linear function of stochastic variable to model random delays, e.g., [1], [24], or random packet dropouts, e.g., [21], [25]; the other one is to use the Markovian chains to model random delays, e.g., [26], [27], or random packet dropouts, e.g., [28], [29]. 3) Switched system method provides a powerful tool for modeling of an NCS with time delays and packet dropouts due to the fact that, whether the transmission of a data packet is successful or not, the switching and delay characteristics of the NCS are obvious, and thus, a switched system model can naturally capture the properties of the NCS with time delays and packet dropouts, e.g., [22], [30]−[32]. In the aforementioned results concerning NCSs with NIDs & PDs, it should be pointed out that a time delay system method mixes the packet dropouts with the delay term, the effects of dropouts are not clearly formulated. On the other hand, a stochastic system method mainly focuses on the discrete system model of NCSs, and more importantly, it is usually assumed that the NIDs & PDs meet certain probability distributions. A switched system method, which has made great advances in the study of the theories and methods [33]−[36], has found a good application for NCSs [22], [30], [31]. However, to the best knowledge of authors, existing results concerning NCSs suffering from NIDs & PDs have mainly focused on either delay or switching behaviors [30], [37]. The coexistence and interaction of switchings and delays in an NCS due to NIDs & PDs, which leads to a more compli- cated stability analysis, have not been fully studied [38]. The importance of the study of this issue, arises from the natural property of the NCS, and the requirement of performance improvement of the system. This motivates the present study.