We investigate the cooperatability of the first-order leader-following multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies. Each agent exhibits first-order linear dynamics, and there are multiplicative noises along with information exchange among the agents. What is more, the communication topologies are Markov switching topologies. By utilizing the stability theory of the stochastic differential equations with Markovian switching and the Markov chain theory, we establish the necessary and sufficient conditions for the cooperatability of the leader-following multi-agent systems. The conditions are outlined below: (ⅰ) The product of the system parameter and the square of multiplicative noise intensities should be less than 1/2; (ⅱ) The transition rate from the unconnected graph to the connected graph should be twice the system parameter; (ⅲ) The transition rate from the connected graph to the unconnected graph should be less than a constant that is related to the system parameter, the intensities of multiplicative noises, and the transition rate from the unconnected graph to the connected graph. Finally, the effectiveness of our control strategy is demonstrated by the population growth systems.

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We study cooperative output feedback tracking control of stochastic nonlinear heterogeneous leader-following multi-agent systems. Each agent has a continuous-time stochastic nonlinear heterogeneous dynamics with an unmeasurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose admissible distributed observation strategies for estimating the leader's and the followers' states, and admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochastic analysis, we show if the dynamics of each agent satisfies the Lipschitz condition, and the product of the leader's Lipschitz coefficient, the intensity of multiplicative measurement noises, and the constant related to the leader's Lipschitz coefficient and dimension is less than 1∕4 the minimum nonzero eigenvalue of graph Laplacian, then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking. Finally, the effectiveness of our control strategies is demonstrated by a numerical simulation. K E Y W O R D Sadditive and multiplicative measurement noise, heterogeneous multi-agent system, mean square bounded output tracking, nonlinear dynamics INTRODUCTIONIn recent years, many scholars have studied the distributed cooperative control of multi-agent systems in precise communication environments. 1-5 However, when each agent interacts with its neighbors through the communication network, communication processes are inevitably interfered by random noises due to uncertain communication environment. Now, more and more researchers pay attention to distributed cooperative control of multi-agent systems with random communication noises. The research on cooperative control of linear multi-agent systems with noises has reached a reasonable degree of maturity. 6-10 Some scholars have studied nonlinear multi-agent systems with additive noises. [11][12][13] investigated fixed-time consensus of first-order nonlinear multi-agent systems. By Lyapunov theory, Xiong et al. 12 studied fixed-time consensus of second-order nonlinear multi-agent systems. Li et al. 13 investigated cluster consensus of high-order nonlinear multi-agent systems under the Markovian topology. Compared with additive noises, multiplicative noises play a stabilizing role in the almost sure stability of systems. 14 There have been some results for nonlinear multi-agent systems 7154