Stabilization of Networked Control Systems Subject to Consecutive Packet Dropouts: The Random Clock Offsets Case

Abstract

In this article, the stabilization problem is investigated for a class of networked control systems with random clock offsets and consecutive packet dropouts. Different from the existing literature, the consecutive packet dropouts occurring in communication networks are subject to clock offsets, and the clock offsets between the sensor and the controller are described by a random variable with a certain probability distribution. First, we construct a closed-loop discrete-time stochastic system by considering the random clock offsets and the consecutive packet dropouts in a unified framework. To render the discrete-time system suitable for analysis, an equivalent yet tractable stochastic augmented model is then established, where the system matrix is characterized by high nonlinearity and dual randomness, which poses substantial difficulties for the expectation operation in the controller design process. In order to deal with the difficulties, the law of total expectation, confluent Vandermonde matrix, and Kronecker product operation are introduced and then a stability condition in the form of linear matrix inequality is obtained. Based on this, a desired controller is designed, such that the closed-loop stochastic system is stochastically stable. Finally, a numerical example with two cases and an example using batch reactor are provided to demonstrate the effectiveness of the proposed design approach.