Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises
For researchers in multi-agent systems and control theory, this work provides rigorous consensus conditions for systems with both delays and noises, addressing a known gap in the literature.
This paper establishes necessary and sufficient conditions for stochastic consensus in continuous-time multi-agent systems with time-delays and measurement noises, covering both additive and multiplicative noise cases. Key results include conditions for weak and strong consensus, with explicit dependence on control gain, noise intensities, and time-delays.
This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations. By the martingale convergence theorem, we obtain necessary conditions and sufficient conditions for stochastic strong consensus. For the case of multiplicative noises, we consider two kinds of time-delays, appeared in the measurement term and the noise term, respectively. We first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus. Then by constructing degenerate Lyapunov functional, we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time-delay in the measurement term.