Stability of linear dynamic systems over the packet erasure channel: a co-design approach

Abstract

This paper is concerned with the stability of linear time-invariant dynamic systems over the packet erasure channel subject to minimum bit rate constraint when an encoder and a decoder are unaware of the control signal. This assumption results in co-designing the encoder, decoder and controller. The encoder, decoder, controller and conditions relating transmission rate to packet erasure probability and eigenvalues of the system matrix A are presented for almost sure asymptotic stability of linear time-invariant dynamic systems over the packet erasure channel with feedback acknowledgment. When the eigenvalues of the system matrix A are real valued, it is shown that the obtained condition for stability is tight. Simulation result illustrates the satisfactory performance of the proposed encoder, decoder and controller for almost sure asymptotic stability.

Keywords:

• networked control system
• almost sure stability
• packet erasure channel

Acknowledgements

This work was supported by the research office of Sharif University of Technology.

Disclosure statement

No potential conflict of interest was reported by the author.