**9. References**


© 2012 Shen and Zhang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Shen and Zhang, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Identifiability of Quantized Linear Systems** 

On-line parameter identification is a key problem of adaptive control and also an important part of self-tuning regulator (STR) (Astrom & Wittenmark, 1994). In the widely equipped large-scale systems, distributed systems and remote systems, the plants, controllers, actuators and sensors are connected by communication channels which possess only finite communication capability due to, e.g., data loss, bandwidth constraint, and access constraint. From a heuristic analysis perspective, the existence of communication constraints has the effect of complicating what are otherwise wellunderstood control problems, including the traditional methods, such as the *H* control (Fu & Xie, 2005), and even the basic theoretic notions, such as the stability (De Persis &

Due to the constraints of the communication channels, it is difficult to transmit data with infinite precision. Quantization is an effective way of reducing the use of transmission resource, and then meeting the bandwidth constraint of the communication channels. However, quantization is a lossy compression method, and hence the performance of parameter identification, even the validity or effectiveness of identification may be changed by quantization, along with which the performance of adaptive control may deteriorate. This has attracted plenty of works. The problem of system identification with quantized observation was investigated in (Wang, et al, 2003, 2008, 2010), where issues of optimal identification errors, time complexity, optimal input design, and the impact of disturbances and unmodeled dynamics on identification accuracy and complexity are

In the light of the fundamental effect of quantization on system identification, it is necessary to pay attention to the parameter identifiability property of quantized systems. The concept of identifiability has been defined by maximal information criterion in (Durgaryan & Pashchenko, 2001): the system is parameter identifiable by maximal

Ying Shen and Hui Zhang

http://dx.doi.org/10.5772/39274

**1. Introduction** 

Mazenc, 2010).

included.

Additional information is available at the end of the chapter
