Decentralised configuration with integral control action is the most commonly used control strategy in engineering practice. For decentralised integral control, a desired design target is to achieve closed-loop unconditional stability. Campo and Morari presented steady-state conditions, which can be applied to analyse unconditional stability for most multivariable processes. However, they also showed some processes for which the unconditional stability cannot be determined by only investigating the steady-state gain matrices of the processes. This paper presented an easy to use criterion to determine unconditional stability by using singular perturbation analysis and eigen-value sensitivity analysis. Based on the proposed criterion, the unconditional stability of all the examples presented by Campo and Morari can be easily determined. In the meantime, we proved a conjecture proposed by Campo and Morari (a necessary and sufficient condition for Integral Controllability) for up to all Three-Input and Three-Output systems. For higher dimensional systems, we proposed a new conjecture to simplify the verification of Campo and Morari's conjecture.