Robust H∞ control of multi-systems with random communication network accessing

This paper studies the robust H∞ control of multi-systems with random communication network accessing. The whole system consists of several sub-systems, which connect with each other via a communication network. These sub-systems have their own states, sensors, controllers and actuators. At each time interval, only part of the sub-systems can get the permissions to use the network. The states of such sub-systems are sent to each other and will experience time delays and quantization errors. This consideration is widely appeared in channel multiplexing systems. The communication network accessing situation and the network-induced time delays are modeled as two different Markov chains. The quantization errors are represented as convex poly-topic uncertainties. By using the Lyapunov-Krasovskii (L-K) functional approach, sufficient conditions on the existence of a mode-dependent controller for this kind of system are presented in terms of bilinear matrix inequalities (BMIs). Furthermore, a cone complementarity algorithm is also presented to convert these BMIs into a convex optimization problem. Finally, a simulation example is given to demonstrate the efficiency of the proposed method.