Stochastic finite-time consensualisation for Markov jump networks with disturbance

This study is devoted to the finite-time consensus control for directed networks with stochastic Markov jump topologies and external disturbances. The purpose of the study is to design a control protocol to ensure that the disagreement dynamics of interconnected networks stay in a given bound over a finite-time interval rather than asymptotically converge to zero in infinite settling time. Through utilisation of certain features of Laplacian matrix in real Jordan form, sufficient conditions for the existence of finite-time consensus protocol is derived by allowing Lyapunov function to increase in a fixed-time interval. Finite-time convergence result for stochastic consensus problem is validated via a simulation study.