Non‐fragile robust control for networked control systems with long time‐varying delay,randomly occurring nonlinearity,and randomly occurring controller gain fluctuation

This paper investigates the non‐fragile robust control problem for a class of nonlinear networked control systems (NCSs) with long time‐varying delay. Both the uncertain nonlinearity and the controller gain fluctuation enter into the system in random ways, and such randomly occurring nonlinearity and randomly occurring controller gain fluctuation obey certain mutually uncorrelated Bernoulli distributed white noise sequences. A new time‐varying discrete time system model is proposed to describe the NCS. To reduce conservatism arising from modeling time‐varying parts, the time‐varying parts due to the time‐varying delay are treated as a norm‐bounded uncertainty with one nominal point using robust control techniques. Based on the obtained uncertain system model, a regular and an optimal sufficient non‐fragile controllers are derived by applying the Lyapunov stability theory and the linear matrix inequality technique, which render the closed‐loop NCS to be asymptotically stable and guarantee an upper bound of the given performance cost for all admissible uncertainties. Moreover, the existence condition and design method for the non‐fragile stabilizing controllers are also presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.