# EECI09: Quantization and bandwidth limits

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In this lecture, we consider networked control over a digital noiseless channel. The one block design problem is largely unsolved. For the two block design problem, the fundamental result is the data rate theorem, which constrains the data rate required for stabilizing the process. There are interesting issues that arise if further constraints are placed on the memory of the encoder.

## Lecture Materials

- Lecture slides: Lecture Summary

## Further Reading

"Feedback control under data rate constraints: an overview", G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, Proceedings of the IEEE, vol. 95, no. 1, pp. 108-37, Jan. 2007. This paper gives a nice overview and provides several references for the general area of control over digital noiseless channels.

Control Under Communication Constraints Sekhar Tatikonda, Ph.D. Thesis, MIT. Some of the performance related issues are discussed in this work.

Stabilizing a linear system with quantized state feedback, D. F. Delchamps, IEEE Transactions on Automatic Control AC-35: 916-924. This work is one of the earlier works to point out the inadequacy of additive white noise approximation of the quantization error.

## Additional Information

- Networked Control Systems Repository (M. Branicky and S. Phillipps)
- 2008 lecture page
- Additional links to external information