In this paper, we propose a distributed consensusbased control method that guarantees agent states limitation for networks of multi-agent systems with undirected communication graphs. This approach takes into account the general linear dynamic models of n identical agents and, by employing Lyapunov methods and ultimate boundedness theory, it ensures that each agent state remains within given bounds. This latter feature is particularly useful in scenarios where one must mitigate the occurrence of abnormal values being transmitted within the network, thus, maintaining a relatively safe consensus policy between agents. The developed strategy requires, at each agent node, information from their respective neighbours only, and it can be applied independently of any global information of the communication graph, hence, it is fully distributed. To highlight the developed controller capability and effectiveness, a multi-converter microgrid system with a meshed communication network has been used as a practical example. Subsequent to the asymptotic stability proof for the overall closed-loop microgrid system, the control framework has been tested in a predetermined scenario.