Open AccessFixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems
Author(s) -
Yu Jiaju,
Yu Shuanghe,
Yan Yan
Publication year - 2021
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/cth2.12040
Subject(s) - settling time , nonlinear system , correctness , fixed point , mathematics , stability (learning theory) , control theory (sociology) , multi agent system , directed graph , computer science , mathematical optimization , discrete mathematics , control (management) , algorithm , mathematical analysis , physics , quantum mechanics , control engineering , machine learning , artificial intelligence , engineering , step response
The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results.