Robust passivity based resilient H_∞ control for networked control systems with random gain fluctuations

The problem of resilient H_∞ controller design for a class of networked control system based on passivity theory is presented. By using the Lyapunov-Krasovskii stability theory and linear matrix inequality approach, a set of sufficient conditions for the existence of state feedback controllers is derived. The networked control system under consideration is modeled by taking the network-induced imperfections like packet dropouts and transmission delays as a single time-varying delay. The controller is considered with a stochastic fluctuations in its gain matrix by using the Bernoulli distributed white sequence with time-varying probability measures. The probability-dependent sufficient conditions are established to guarantee the resulting closed-loop system to be stochastically stable with a prescribed mixed H_∞ and passivity performance criterion. The results are expressed in the form of convex optimization problem subject to the set of LMIs, which can be easily solved by using some standard numerical packages. Finally, a numerical example by using the high-incidence research model is presented to illustrate the effectiveness and applicability of the theoretical results.