Stabilization of Networked Control Systems Subject to Noisy Sampling Intervals and Stochastic Time-Varying Delays

In practical engineering, the sampling intervals of networked control systems are often subject to undesirable physical constraints, which results in noisy sampling intervals. In view of this, we focus on the linear plants without unknown parameters and investigate the stabilization problem of networked control systems with noisy sampling intervals and stochastic time-varying delays. First, a closed-loop discrete-time stochastic system, whose system matrices are characterized by high nonlinearity and randomness, is obtained by considering the noisy sampling intervals and stochastic time-varying delays in a unified framework. Second, an equivalent yet tractable stochastic-augmented model is established with the aid of matrix exponential computation. With a confluent Vandermonde matrix associated with the minimal polynomial and Kronecker product operation, the mathematical expectation of a product of three matrices, including the system matrix of the stochastic-augmented model and its transpose, is calculated. Based on this, a stabilization controller is designed such that the stochastic stability of the original discrete-time stochastic system is guaranteed. Finally, an illustrative example with four different cases is provided to verify the effectiveness of the designed method.