Random sampling and performance analysis for networked systems

This paper investigates networked control systems using random sampling method which can be tuned by a continue time Markov chain. The sampling instants are modeled by using jumps between states of a continue time Markov chain. Whenever there is a jump from a state in the Markov chain to a state that represent a subsystem in the networked system, we sample that particular subsystem and transmit its state measurement across the shared communication network to the corresponding sub-controller. By minimizing a cost function which was introduced for this Markov Chain, we extract an optimal scheduling policy to fairly allocate the network resources among the subsystems. The statistical properties of this scheduling policy are studied to compute upper bounds for the closed-loop performance of the networked system. A numerical example has shown the usefulness of the proposed results.