On the basis of the Passivity Theorem, this paper provides a new approach to stability analysis for multi-loop control systems. The destabilizing effect of interactions of a multi-input multi-output system is studied using the passivity index. The decentralized unconditional stability condition, which implies closed-loop stability of decentralized control systems under control loop failure, is derived. An easy-to-use stability test is performed on open-loop stable process transfer matrices, independent of controller designs.