Interconnection is omnipresent in a system through the state variables and induced for multi-system interaction and shared tasks. Typically, the example of multi-agent coordination was studied as an interconnected system. The paper deals with the finite-time stability problem of a general form of interconnection presented as a perturbation term. Sufficient conditions for finite-time stability are derived. A second interest is given to the interaction of multiple controlled autonomous systems, and where the multi-system control-input is established both for finite-time stabilization. As an example of application, the finite-time tracking problem of four unicycles is studied.