Finite-Time Consensus of Finite Field Networks With Stochastic Time Delays

This brief aims to solve the finite-time consensus problem of finite field networks (FFNs) with stochastic time delays. An algebraic state space representation (ASSR) approach is introduced for the investigation of this problem. Firstly, the concept of finite-time consensus with probability one is defined for FFNs with two kinds of stochastic time delays. Secondly, the dynamics of FFNs with time delays is converted into an ASSR, based on which, the dynamics of FFNs with probabilistic time delay is converted into a linear discrete-time stochastic system. It is shown that the finite-time consensus of FFNs with probabilistic time delay is equivalent to the finite-time set stability of the obtained system. Thirdly, a verifiable criterion is put forward for the finite-time consensus of FFNs with probabilistic time delay. Finally, using the dummy matrix, the dynamics of FFNs with Markov jump time delay is also converted into a linear discrete-time stochastic system, and the corresponding criterion is proposed for the finite-time consensus of FFNs with Markov jump time delay.