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Minimum information rate for observability of linear systems with stochastic time delay

ABSTRACT This paper investigates the state estimation problem for linear time-invariant systems where sensors and controllers are geographically separated and connected via stationary memoryless uncertain digital communication channels with the information rate limitation. Such channels introduce data packet dropout, stochastic time delay, and data packet reordering. In the TCP/IP model, the transport layer provides a reliable service on top of an unreliable communication channel. However, the performance of such systems is still affected by packet reordering and stochastic time delay. In particular, we present an optimal encoding and decoding scheme to guarantee observability by employing the minimum information rate, and derive a necessary and sufficient condition on the delay distribution and information rate for observability. Illustrative examples are given to demonstrate the effectiveness of the proposed scheme.