Stabilization of networked systems with communication constraints: The random sampling periods case

Abstract

In this paper, the stabilization problem of networked systems with communication constraints is studied, where the random sampling periods, deception attacks and packet losses are considered simultaneously. Different from the existing literature, the actual sampling periods are subject to undesirable physical constraints and fluctuate around an ideal sampling period with certain probability distribution. First, a closed-loop discrete-time stochastic system is constructed by considering the random sampling periods, deception attacks and packet losses in a unified framework. Second, an equivalent yet tractable stochastic model is established with the aid of matrix exponential computation. By reduced-order confluent Vandermonde matrix approach, law of total expectation, convolution formula and Kronecker product operation, a controller is designed such that the exponential stability in the mean-square sense of closed-loop stochastic system is guaranteed. Subsequently, a special model is discussed where no deception attack occurs and then the corresponding controller is designed. Finally, an illustrative example is given to show the effectiveness of the designed approach.