Robust Stability and Disturbance Attenuation Analysis of a Class of Networked Control Systems Hai Lin Department of Electrical Engineering University of Notre Dame Notre Dame, IN 46556, USA Guisheng Zhai Department of Opto-Mechartronics Wakayama University Sakaedani, Wakayama 640-8510, Japan Panos J. Antsaklis Department of Electrical Engineering University of Notre Dame Notre Dame, IN 46556, USA Abstract— In this paper, stability and disturbance attenua- tion issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H ∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to corresponding problems for the switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions. I. INTRODUCTION By Networked Control Systems (NCSs), we mean feed- back control systems where networks, typically digital band- limited serial communication channels, are used for the connections between spatially distributed system components like sensors and actuators to controllers. These channels may be shared by other feedback control loops. In traditional feed- back control systems these connections are through point-to- point cables. Compared with the point-to-point cables, the introduction of serial communication networks has many advantages, such as high system testability and resource utilization, as well as low weight, space, power and wiring requirements [9], [14]. These advantages make the networks connecting sensors/actuators to controllers more and more popular in many applications, including traffic control, satel- lite clusters, mobile robotics etc. Recently modeling, analysis and control of networked control systems with limited com- munication capability has emerged as a topic of significant interest to control community, see for example [4], [3], [6], [14], [1], [9]. Time delay typically has negative effects on the Networked Control Systems’ stability and performance. There are sev- eral situations where time delay may arise. First, transmission delay is caused by the limited bit rate of the communication channels. Secondly, the channel in NCSs is usually shared by multiple sources of data, and the channel is usually multiplexed by time-division method. Therefore, there are delays caused by a node waiting to send out a message through a busy channel, which is usually called accessing delay and serves as the main source of delays in NCSs. There are also some delays caused by processing and propagation, which are usually negligible for NCSs. Another interesting problem in NCSs is the packet dropout issue. Because of the uncertainties and noise in the communication channels, there may exist unavoidable errors in the transmitted packet or even loss 1 . If this happens, the corrupted packet is dropped and the receiver (controller or actuator) uses the packet that it received most recently. In addition, packet dropout may occur when one packet, say sampled values from the sensor, reaches the destination later than its successors. In such situation, the old packet is dropped, and its successive packet is used instead. There is another important issue in NCSs, that is the quantization effect. With finite bit-rate constraints, quantization has to be taken into consideration in NCSs. Therefore, quantization and limited bit rate issues have attracted many researchers’ attention, see for example [3], [6], [4]. It has been known [3], [6] that an exponential data representation scheme is most desirable under certain conditions. In this paper, we consider uncertain time delay and packet dropout issues of NCSs in the framework of switched sys- tems. The strength of this approach comes from the solid theoretic results existing in the literature for stability, robust performance etc. for switched systems. By a switched system, we mean a hybrid dynamical system consisting of a finite number of subsystems described by differential or difference equations and a logical rule that orchestrates switching be- tween these subsystems. Properties of this type of model have been studied for the past fifty years to consider engineering systems that contain relays and/or hysteresis. Recently, there has been increasing interest in the stability analysis and switching control design of switched systems (see, e.g., [10], [5], [11], [12] and the references cited therein). Notice that hybrid/switched system research has provided useful results and promising techniques to deal with NCSs with delay and packet dropout effects. For example, in [14], the multiple Lyapunov function method [2] was employed to analyze the stability of NCSs with network-induced delay. In addition, the packet dropout effects in NCSs are closely related to the controller failures studied in the fault tolerance literature. There are some recent work on the controller failure analysis based on switched system techniques [11], [13]. By using a piecewise Lyapunov function, the author in [13] showed that if the controller failures did not occur too frequently or last 1 Error control coding and/or Automatic Repeat reQuest (ARQ) mecha- nism may be employed, but the possibility of error occurring still exists. Proceedings of the 42nd IEEE Conference on Decision and Control Maui, Hawaii USA, December 2003 TuP06-2 0-7803-7924-1/03/$17.00 ©2003 IEEE 1182