Research on control of network system with Markov delay characteristic

Contraposing to the stochastic transfer delay inherently existing in the control network, a novel control mode is proposed, which implements the modeling of the network control system with multi-step stochastic transfer delay. It is proved that under this control mode, the transfer delay possesses Markov characteristic. Also the method calculating the corresponding Markov state transition matrix is given. Based on the obtained mathematical model, utilizing Markov chain theory, the stochastic optimal control law satisfying the pre-specified performance index is obtained. At the same time, a necessary condition guaranteeing the final mean square stability of the closed system is presented. Simulation at the end of the paper shows the correctness and the validity of the proposed theory