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Applied Mathematics Letters 40 (2015) 35–39

Contents lists available at ScienceDirect

Applied Mathematics Letters

journal homepage: www.elsevier.com/locate/aml

Leader-following exponential consensus of general linear

multi-agent systems via event-triggered control with

combinational measurements

Bo Zhou

, Xiaofeng Liao

a,∗

, Tingwen Huang

, Guo Chen

College of Electronic and Information Engineering, Southwest University, Chongqing 400716, China

Texas A&M University at Qatar, Doha, P.O. Box 23874, Qatar

School of Electrical and Information Engineering, The University of Sydney, Australia

a r t i c l e i n f o

Article history:

Received 8 August 2014

Received in revised form 14 September

2014

Accepted 14 September 2014

Available online 28 September 2014

Keywords:

Event-triggered consensus

Multi-agent systems

General linear systems

Convergence rate

a b s t r a c t

In this paper, the leader-following exponential consensus problem of general linear multi-

agent systems via event-triggered control is considered. By using the combinational

measurements, two classes of event triggers are designed, one depends on continuous

communications between the agents, the other avoids continuous communications. For

such two classes of event triggers, the exponential consensus as well as the convergence

rates of the controlled multi-agent systems are studied, respectively, by employing the

M-matrix theory, algebraic graph theory and the Lyapunov method.

1. Introduction

In this paper, we consider the following multi-agent systems including N agents described by

(t) = Ax

(t) + Bu

(t), i = 1, 2, . . . , N, (1)

where x

(t) ∈ R

and u

(t) ∈ R

denote the state and control input of agent i, respectively. A ∈ R

n×n

and B ∈ R

p×n

are

constant matrices. Let s(t) be the leader, labeled by agent 0, whose dynamical behavior is described as follows

s(t) = As(t). (2)

In multi-agent system (1), the control input u

(t) are event triggered, that is, the control updates are determined by

certain events that are triggered depending on the agents’ behaviors. The event-triggered controllers have been adopted

for control engineering applications, such as the control of memristive systems [1], the control of wireless sensor/actuator

networks [2], and the networked control systems [3,4]. In [5–9], the authors have considered the event-triggered control for

multi-agent systems. Our work mainly builds on the works in [9,8]. In [9], the authors studied the event-triggered control

of integrator multi-agent systems with combinational measurements, in which the graph of communication topology is

undirected. In [8], the authors studied the consensus of general linear multi-agent systems using error-based event triggers.

Compared with the dynamics of integrator multi-agent systems, the dynamics of general linear multi-agent systems are

∗

Corresponding author. Tel.: +86 2368367391.

E-mail address: xfliaoswu@gmail.com (X. Liao).

http://dx.doi.org/10.1016/j.aml.2014.09.009

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