Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay

This paper is concerned with the stochastic bounded consensus tracking problems of leader–follower multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighborhood agents or a virtual leader with a time-varying reference state, the measurements are corrupted by random noises, and the signal sampling process induces a small sampling delay. The augmented matrix method, probability limit theory and algebra graph theory are employed to derive the necessary and sufficient conditions guaranteeing mean square bounded consensus tracking. It turns out that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampling period and the sampling delay, and that the static consensus tracking error depends on not only the above-mentioned factors, but also the noise intensity, the number of agents and the upper bound of the changing rate of the virtual leader’s state. The obtained results cover no sampling delay as a special case. Simulations are provided to demonstrate the effectiveness of the theoretical results.