This paper aims to present a novel constructive framework for the functioning zone assignment of linear heterogeneous Multi-Agent dynamical systems, in order to improve the operation safety in a decentralized manner. The main contributions are related to partitioning the working space of this global system into multiple non-overlapping regions. The construction of the partition is mainly based on the desired position of each agent in a predefined formation and subject to constraints related to the local dynamics of the agents. Each region is assigned to one agent and subsequently guaranteed to be control invariant by applying an optimization-based decentralized control. A numerical example will be shown in order to prove the effectiveness of the proposed approaches.