Mean-square consensus of discrete-time multi-agent systems with Markovian switching topologies and persistent disturbances

Lipo Mo,Yintao Wang,Tingting Pan,Yikang Yang

doi:10.1177/1550147717726313

Abstract

This article deals with the leader-following mean-square consensus problem of discrete-time general linear multi-agent systems with Markovian switching topologies and persistent disturbances. Assume that the communication topology is not connected at any time but the union topology is connected. First, the estimators are designed to calculate the states of agents when external disturbance not exists. Based on the error information between the truth-values and estimated-values of states, the compensators are proposed to subject to the effect of persistent disturbances. And then, a new mean-square consensus control protocol is proposed for each agent. Second, by using the property of permutation matrix, the original closed-loop system is transferred into an equivalent system. Third, sufficient conditions for mean-square consensus are obtained in the form of matrix inequalities. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

Highlights

The distributed coordination control problems of the multi-agent systems have attracted intensive attention from different fields’ scholars
The consensus problem is the essential problem in the distributed coordination control field
The output consensus problem was studied for a class of uncertain linear multi-agent systems.[5]

Summary

Introduction

The distributed coordination control problems of the multi-agent systems have attracted intensive attention from different fields’ scholars. Zhang and Tian[13] proved that the switching systems can realize mean-square consensus when the union of graphs has a globally reachable node. Cheng et al.[15] studied the mean square and almost sure consensus problem of discrete-time linear multi-agent systems with communication noises and Markovian switching topologies. A new control protocol was proposed to drive the multi-agent system with persistent disturbances to achieve mean-square consensus when the topology switches stochastically among some unconnected graphs, and the switch is driven by an ergodic Markovian chain. We consider the multi-agent systems with stochastically switching topologies provided that the union of topologies has a globally reachable node. The purpose of this article is to study the meansquare leader-following consensus condition for multiagent systems with persistent disturbances and the Markovian switching topologies. The above three equations can be written in the following matrix form e(k + 1)

A À BfK s

A À BcK s

A À liBK

A À liBK and