Stability of linear feedback systems with random communication delays

Abstract

Integral control of large-scale systems implies coordination of activities by information exchange via communication networks. Usually these networks are shared with other users. Thus traffic conditions in the network may introduce time-varying random delays in the control loop with adverse effects on its performance and stability. Hence, the control must be designed to compensate for these delays. Recent work in modelling integrated control and communication systems has shown that the communication specific phenomena inducing random communication delays (such as multirate sampling, vacant sampling and message rejection) may be encompassed by finite-dimensional linear discrete-time models, provided that the plant and the controller are linear and time invariant. Existing approaches to the design of integrated control systems rely on conservative stability tests, because only sufficient stability conditions were found for systems with random time-varying delays. In this paper, necessary and sufficient conditions are found for zero-state mean-square exponential stability of the considered class of control systems. Numerical tests for zero-state stability are outlined and illustrated by a simple example. Finally, the results are also demonstrated on specific hardware, a multiprocessor real-time control network which has been recently developed.