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\(H^{\infty }\) control with limited communication and message losses. (English) Zbl 1133.93016
Summary: We propose an \(H^{\infty }\) approach to a remote control problem where the communication is constrained due to the use of a shared channel. The controller employs a periodic time sequencing scheme for message transmissions from multiple sensors and to multiple actuators of the system. It further takes into account the information on the random message losses that occur in the channel. An exact characterization for controller synthesis is obtained and is stated in terms of linear matrix inequalities. Furthermore, an analysis on the loss probabilities of the messages to accomplish stabilization is carried out. The results are illustrated through a numerical example.

MSC:
93B36 \(H^\infty\)-control
93E03 Stochastic systems in control theory (general)
93B50 Synthesis problems
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