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

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 encoder and decoder are unaware of control signal. This assumption results in co-designing encoder, decoder and controller. 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.