Consensus Control of Singular Stochastic Multi-Agent Systems with State-Dependent Noise

In practical settings, noise significantly affects the consensus of singular multi-agent systems. This paper addresses the consensus problem for singular stochastic multi-agent systems with state-dependent noise, leveraging the consensus theory of singular stochastic systems and relevant theories. A consensus control protocol based on state feedback is proposed, transforming the system into the restricted equivalence form. By integrating the generalized Lyapunov inequality of stochastic differential equations, a linear matrix inequality is derived. Rigorous analysis yields the conditions for the protocol to achieve mean square consensus, thereby resolving the mean square consensus issue for such systems under state-dependent noise. The paper offers novel theoretical methodologies and technical support for the consensus control of singular multi-agent systems in complex noisy environments, carrying significant theoretical and practical implications.