Sign-Consensus of Linear Multiagent Systems under a State Observer Protocol

Wei-Lu Diao,Cui-Qin Ma

doi:10.1155/2019/3010465

Wei-Lu Diao, Cui-Qin Ma

Open Access

https://doi.org/10.1155/2019/3010465

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Journal: Complexity	Publication Date: Nov 3, 2019
Citations: 2	License type: CC BY 4.0

Affiliation: Qufu Normal University

Abstract

The sign-consensus problem for linear time-invariant systems under signed digraph is considered. The information of the agents’ states is reconstructed, and then, a state observer-type sign-consensus protocol is proposed, whose performance is analyzed using matrix analysis and ordinary differential equation theory. Sufficient conditions for ensuring sign-consensus are given. It is proven that if the adjacency matrix of the signed digraph has strong Perron–Frobenius property or is eventually positive, sign-consensus can be achieved under the proposed protocol. In particular, conventional consensus is a special case of sign-consensus under mild conditions.

Highlights

Consensus, as the key to coordination of multiagent systems (MASs), has been investigated extensively in recent years [1,2,3,4,5,6,7,8,9]
It is shown that signconsensus can be reached if the graph adjacency matrix is frequently eventually positive
In this work, we investigate signconsensus for LTI MASs under signed digraphs. e agents’ states are reconstructed, and state observer-type protocols based on them are given

Summary

Introduction

As the key to coordination of multiagent systems (MASs), has been investigated extensively in recent years [1,2,3,4,5,6,7,8,9]. In the pioneering work [23], it is shown that, for the linear timeinvariant (LTI) MASs, if the graph adjacency matrix is eventually positive, sign-consensus is achieved under a state feedback sign-consensus protocol and a fully distributed sign-consensus protocol, respectively. It is shown that signconsensus can be reached if the graph adjacency matrix is frequently eventually positive We notice that both works [23, 24] propose state feedback-type sign-consensus protocols. It would be more convenient to synthesize consensus protocols based on the agents’ state estimates With these observations, in this work, we investigate signconsensus for LTI MASs under signed digraphs. It is shown that if the graph adjacency matrix has strong Perron–Frobenius property or is eventually positive, sign-consensus for LTI MASs can be achieved. For A ∈ Rn×n, A has the strong Perron–Frobenius property ⟺ A is eventually positive

Problem Formulation

Main Results

Simulation