This paper is concerned with detection and diagnosis of modelling error under closed-loop conditions. The effect of modelling error on process output error (which is the error between the process output and the simulated output) is first analysed. Then robust stability conditions for on-line model validation are applied. The main premise is that whenever the closed-loop system violates the robust stability condition, it is a sign of significant process change and a signal that the control system may become potentially unstable. We relate the process output error with robust stability conditions and introduce three propositions for on-line model validation. Any process change (or modelling error) that makes the system violate the condition specified by the robust stability theorem can be detected. Simulation examples are presented to demonstrate the applicability of the propositions. An index is also proposed to quantify modelling error in frequency domain. Simulation examples and an experimental case study are presented to demonstrate the use of the new index.