Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.

Linear impulsive control system with impulse time windows

We formulate the linear impulsive control systems with impulse time windows. Different from the most impulsive systems where the impulses occur at fixed time or when the system states hit a certain hyperplane, the impulse time in the presented systems might be uncertain, but limited to a small time interval, i.e. a time window. Compared with the existing impulsive systems, the systems with impulse time windows is of practical importance. We then study the asymptotic stability of the case of linear systems and obtain several stability criteria. Numerical examples are given to verify the effectiveness of the theoretical results.