Mean square and almost sure consensus of heterogeneous multi-agent systems with multiplicative noise

This paper studies the consensus problem of heterogeneous multi-agent systems (MASs) composed of first-order and second-order agents. To describe the communication environment realistically, the effect of the multiplicative noise on the communication network is considered. Firstly, the consensus problem is transformed into the stability problem of stochastic differential equations with multiplicative noise. Then, a stability analysis method for such stochastic differential equations is proposed by structuring the appropriate Lyapunov function. Some sufficient conditions for both mean square (m.s.) and almost sure (a.s.) consensus are obtained for leader-free/leader-following heterogeneous MASs. These sufficient conditions, expressed by simple scalar inequalities, are explicitly related to control gains, noise intensities, and network topology. Furthermore, the m.s. and a.s. convergence rates of the consensus protocol are also obtained. Finally, numerical simulation shows the effectiveness of our theoretical results.