Robust mixed H₂/H_∞control of networked control systems with random delays and partially known transition matrix

A robust two-mode-dependent controller is discussed in this paper for a special jump linear networked control systems. Delays of random nature exist in both measurement channel (C/A) and actuation channel (S/C). These delays are modeled through two homogeneous independent Markov chains. Terminologies for the norms of H₂ and H_∞for such systems are also given. The two mode dependent output feedback control law is proposed, which means that its value depends on the current delay existing in measurement channel and also on the previous delay in actuation channel. Further more, a robust H₂ and robust mixed H₂/H_∞ controllers are developed for networked control systems (NCSs). Similar analyses and design procedures are also carried out for the case of partially known transition probability matrices. In the end, a numerical example is presented and comparison is made between the results obtained in this paper and the stability criteria developed by Zong et al. [11] to illustrate the effectiveness of the developed methodology.