Open AccessStochastic finite‐time consensualisation for Markov jump networks with disturbance
Author(s) -
Luan Xiaoli,
Min Yang,
Ding Zhengtao,
Liu Fei
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.1265
Subject(s) - settling time , control theory (sociology) , convergence (economics) , mathematics , interval (graph theory) , markov chain , lyapunov function , laplacian matrix , markov process , upper and lower bounds , consensus , mathematical optimization , computer science , laplace operator , control (management) , multi agent system , mathematical analysis , engineering , statistics , physics , artificial intelligence , quantum mechanics , combinatorics , control engineering , nonlinear system , economics , step response , economic growth
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.