Observability and controllability of systems with limited data rate

Abstract

Some fundamental properties of observability and controllability are studied for linear discrete-time systems in a bandwidth-limited communication network environment shared by a number of sensors and actuators and a remote controller. The concepts of finite time set-observability and set-controllability are introduced for such systems. Sufficient and necessary conditions on quantisation level for set-observability and set-controllability are derived. Especially, the admissible data rates of the communication network are obtained that are sufficient and necessary for the system to be finite time set-observable or finite time set-controllable. In addition, less conservative sufficient and necessary rates based on quantisation level of system states are given too.

Keywords:

• set-observability
• set-controllability
• communication capacity
• linear control systems

Acknowledgements

The author would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. This work was supported by National Natural Science Foundation of China under grant number 60504017, Fok Ying Tong Educational Foundation under grant 111066 and Program for New Century Excellent Talents in Universities of China under grant NCET-04-0982.