Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

Yingming Tian,Yi Chai,Yangquan Chen,Qin Xia,Liping Chen,António M Lopes

doi:10.3390/fractalfract5040141

Abstract

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.

Highlights

The main contributions are the following: (1) to address the guaranteed cost consensus for nonlinear FOMASs with state and input time delay; (2) to establish in terms of linear matrix inequality (LMI) a delay-dependent and order-dependent sufficient condition for guaranteed cost leaderless consensus protocol; and (3) to obtain a guaranteed cost leaderless consensus protocol less conservative than the ones already proposed in the literature
We introduce basic concepts of graph theory, definitions related to fractional calculus, guaranteed cost function related to FOMASs and some useful lemmas
A delay-dependent sufficient condition for the guaranteed cost consensus protocol is established in terms of LMI, and its guaranteed cost is derived

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It should be pointed out that most research has been focused on IO MASs instead of FOMASs and, in particular, the guaranteed cost consensus of FOMASs with state and input time-delay receiveed limited attention. Motivated by the above discussion, a guaranteed cost leaderless consensus protocol for uncertain nonlinear delayed FOMASs with input time delay is proposed in this paper. The main contributions are the following: (1) to address the guaranteed cost consensus for nonlinear FOMASs with state and input time delay; (2) to establish in terms of linear matrix inequality (LMI) a delay-dependent and order-dependent sufficient condition for guaranteed cost leaderless consensus protocol; and (3) to obtain a guaranteed cost leaderless consensus protocol less conservative than the ones already proposed in the literature. The matrices A T and A−1 denote the transpose and inverse of A, respectively

Graph Theory

Useful Lemmas

Problem Statement

Main Results

Numerical Simulations

Conclusions