$H_{\infty}$ Consensus of Linear Multi-Agent Systems With Semi-Markov Switching Network Topologies and Measurement Noises

Meiyan Cong,Xiaowu Mu

doi:10.1109/access.2019.2949282

Abstract

This paper investigates the H∞ consensus of linear multi-agent systems with semi-Markov switching network topologies and measurement noises. The information that each agent measures its neighbors's has multiplicative noises. The switching of the network topologies are modeled by a semiMarkov process. Taking the external disturbance into account, H∞ consensus of multi-agent systems with multiplicative noises is achieved under semi-Markov switching network topologies by using semi-Markov jump theory, stochastic theory and algebraic graph theory. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results.

Highlights

More and more attention has been paid to the distributed coordination of multi-agent systems in recent years
The main contributions of this paper are summarized as follows: (1) compared with the existing works with Markov switching topologies, communication topologies in our paper are semi-Markov switching topologies, which is more general and challenging due to that the transition rates of semi-Markov switching are time-varying. (2) in practical application, networked systems are often in uncertain environments and are inevitably affected by measurement noises, our paper considers the effects of measurement noises, which is different from the existing literatures with semi-Markov switching topologies and make the analysis more difficult since the traditional definitions and methods are not applicable to our problems due to the existence of randomness. (3) taking the effects of external disturbances into consideration, H∞ consensus is investigated in our paper
For a given index δ > 0, the H∞ consensus of linear multiagent systems (2) and (4) with semi-Markov switching network topologies can be solved if there exist matrices P(k) to guarantee the following matrix inequalities: (k) =

Summary

INTRODUCTION

More and more attention has been paid to the distributed coordination of multi-agent systems in recent years. To the best of our knowledge, consensus problem of multi-agent systems with measurement noises under semi-markov switching topologies still remains open and challenging, which is the first motivation of our study. Based on the aforementioned works and the need to fill the gaps, in this paper, we discuss the H∞ consensus of linear multi-agent systems with semi-markov switching network topologies and measurement noises by using semi-markov jump theory, stochastic theory and algebraic graph theory. (2) in practical application, networked systems are often in uncertain environments and are inevitably affected by measurement noises , our paper considers the effects of measurement noises, which is different from the existing literatures with semi-Markov switching topologies and make the analysis more difficult since the traditional definitions and methods are not applicable to our problems due to the existence of randomness. For a given random variable or vector x, E(x) represents its mathematical expectation

GRAPH THEORY

SEMI-MARKOV SWITCHING TOPOLOGY

MAIN RESULTS Theorem 1

SIMULATION RESULT

CONCLUSION