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Stability of linear feedback systems with random communication delays. (English) Zbl 0812.93073
Integral control of large-scale systems implies coordination of activities by information exchange via communication networks. 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. Finite-dimensional linear discrete-time models can represent these large- scale systems provided that the plant and the controller are linear and time invariant. Here, 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.

MSC:
93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
93B52 Feedback control
93A15 Large-scale systems
34K35 Control problems for functional-differential equations
93D20 Asymptotic stability in control theory
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