ROBUST H∞ OUTPUT TRACKING CONTROL WITH PARTLY QUANTIZED INFORMATION Yang Ge, Jingcheng Wang, Langwen Zhang, and Chuang Li ABSTRACT This paper is concerned with the stability and output tracking problems of networked control systems (NCSs) with partly quantized information. Both the remote and local systems are considered. The state variables transported from the remote system experiences time delays and quantization errors, while the local state variables do not. The purpose is to design a state feedback controller which guarantees that the output of the local system tracks the output of the remote system in the H∞ sense. This consideration is widely appeared in remote assistant systems. Based on the Lyapunov–Krasovskii (L-K) functional approach, sufficient conditions on the existence of a quantized robust H∞ output tracking controller for NCSs are presented in terms of bilinear matrix inequalities (BMIs). Furthermore, a cone complementarity algorithm is used to convert these BMIs into a convex optimization problem. Finally, a simulation example is given to demonstrate the efficiency of the proposed method. Key Words: Networked control systems, H-inf control, output tracking, partly quantized. I. INTRODUCTION Networked control systems (NCSs) are defined as distributed control systems in which control loops are closed through real time network. Although NCSs have a lot of advantages, various constraints such as time delays and packet dropouts may occur due to the incorporation of a network in control loops. Moreover, quantization errors caused by the limited bandwidth may deteriorate the perfor- mance of the whole system [1]. The problem of network-induced time delays is one of the most important problems in NCSs. In most cases, it cannot be averted due to the distributive nature of controllers and plants. Many results focusing on this problem have been investigated [2–8]. These approaches can usually be classified as deterministic or stochastic. Deterministic approaches as- sume the time delays are bounded and the purpose is to find the maximum delays which can be tolerated [2,3]. Stochastic approaches assume time delays follow certain probability distributions, such as Markov chain or Bernoulli random sequences, and try to prove mean square stability [4–8]. The problem of quantized feedback control has attracted a growing research interest in recent years. The problems of stability analysis and controller synthesis of NCSs with quantizers were first addressed in [9]. From then on, two main classes of quantizers, the uniform quantizers and the non-uniform quantizers, have been considered. For the uniform quantizers, the quantization levels are fixed for all inputs [10,11], while the quantization levels of non- uniform quantizers change as the inputs change [12–15]. It has been shown that the minimum quantization informa- tion required for a quantized control system to be stable depends on the unstable poles of the open-loop system [16]. In [17], it was pointed out that the classical sector bound approach was non-conservative for quantizer design. Tracking control, as an important issue in the control field, has been extensively applied in industry, such as flight control, robot control, signal processing and other practical fields [18–26]. The aim is to force the controlled output to follow a desired reference signal under effective control. Many results have been reported on this issue. In [19], the problem of H∞ output tracking for network-based control systems was investigated. An LMI-based procedure was proposed, which guaranteed the tracking performance. In [22], the tracking problem for discrete-time networked pre- dictive control systems was discussed. The Luenberger ob- server was used and network-induced time delays on both links were considered. Reference [24] investigated the PID control problem in the NCS scheme. A novel technique was proposed to convert the PID controller design problem into an output feedback controllers design problem. However, the above literature is based on the assump- tion that a network exists between the plants and the con- troller. That is, the network-induced factors will affect both the physical plant and the reference model. In some Manuscript received July 4, 2013; revised December 4, 2013; accepted February 16, 2014. The authors are with the Department of Automation, Shanghai Jiao Tong Univer- sity and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai Jiao Tong University, Shanghai, 200240, China. Jingcheng Wang is the corresponding author (e-mail: jcwang@sjtu.edu.cn). The authors thank the anonymous reviewers for their valuable comments and sug- gestions to improve the quality of the paper. This work was supported by National Natural Science Foundation of China (no. 61174059, 61233004), National 973 Program of China (no. 2013CB035406), Research Project of Shanghai Municipal Economic and Informatization Commission (ZB-ZBYZ-01112634, 12GA-31). Asian Journal of Control, Vol. 17, No. 3, pp. 1–12, May 2015 Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/asjc.958 © 2014 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd