Robust $H_{\infty}$ Control of Lurie Nonlinear Stochastic Network Control Systems With Multiple Additive Time-Varying Delay Components

In order to further solve the stability problem in the actual network control systems, this paper first simultaneously considers the controlled object system delay and network time delay in the Lurie nonlinear stochastic network control systems. Among them, the controlled object system delay is multi-time delay and the network time delay is two additive time-varying delay component. The proposing of the two additive time-varying delay components in network control systems has advantages in producing less conservatism over the previous one with a combined delay. By employing the method of improved free weighting matrix and constructing a Lyapunov–Krasovskii functional, less conservative robust
$H_{\infty }$
stability criterion is established and the controller is designed for the system in this paper. Some numerical examples are given to demonstrate the applicability of the proposed method.