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An independent stability assurance layer for the multivariable controller in the hierarchical control architecture is introduced in this paper. This stability layer provides an integrated safety and protection measure to process control systems from closed-loop instabilities, which may cause process upsets and shutdowns. It prevents disruptive shutdowns by providing corrective actions to the controller outputs. The Supervisory Stability Layer is established based on the renowned dissipative systems theory. The implementation of this approach is illustrated by an example of stability guarantee of model predictive controllers.