This paper is concerned with the problems of quantized H 00 control for networked control systems with random communication delays. The quantizer considered here is logarithmic type. A quantized state-feedback controller is designed, such that the closed-loop system is exponentially mean square stable in the sense of mean square and achieves an optimal Hoo disturbance attenuation level. Sufficient conditions for exponentially mean-square stable of closed-loop system is given in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed approach.Index Terms-Hoo control, Networked control systems, Ran dom communication delays, Logarithmic quantization, Linear matrix inequalities (LMls).
I. INTRO DUCTIONNetworked control systems (NCSs) have been intensively studied over the past decades because of many advantages in cluding high reliability, low cost and so on. However, since the limited bandwidth of network, there are also some problems of NCSs, such as communication delays, packet dropouts, quanti zation, etc. Thus NCSs have attracted increasing attentions and many methods for solving this problems have been developed in recent literature.Recently, there have been a lot of interests in quantized control, where the feedback signal is quantized and coded for transmission, especially the application in networked control systems. The signals have to be quantized with an appropriate precision when they transmitted by network because of the limited bandwidth of network, digital controllers employed in NCS and so on. Quantization is a common source of errors which may cause the system performance to deteriorate [1]. The investigation of quantization error in digital control systems has been an important area of research.Since quantization always exists in networked control sys tems, many researchers have begun to study the quantized control problems with various methods. There are two types of quantizers are being studied. The first type is static linear time-invariant quantizer. The parameters of the quantizer are fixed in advance and cannot be changed, such as in [1]-[5]. Another type of quantizer is time-variant quantizer, where it is obviously advantageous to the time-invariant quantizer, because it can increase region of attraction and reduce the 978-1-4244-6588-0/10/$25.00 ©201 0 IEEE 513 Iko MIYAZAWA steady state limit cycle by scaling the quantization levels dynamically [7]. Existing work using time-variant quantizers includes [6]-[10]. On the other hand, for a class of NCSs with random communication delays, network delays are usually modeled by Bernoulli random bilinear distribution or Markov Jump Linear Systems. Recently, there have been many significant research results, such as in [11]-[14]. In [11], the communication delays have been assumed to be randomly varying time delays and a test of stochastic stability of the closed-loop system has been presented. In [12], random delays are modeled as a linear function of the stochastic variable satisfying Be...
