New Criterion Enforces Stability in Parametric Model Order Reduction

Preserving stability when reducing complex dynamical systems is a critical challenge, especially when models depend on geometric or physical parameters. Typical algorithms like the Parameterized Sanathanan-Koerner iteration or the pAAA method construct reduced models from sampled transfer function data, but ensuring stability across the entire parameter domain remains difficult. Existing approaches often introduce conservatism, sacrificing accuracy for guaranteed stability.

In a new paper, Antonio Carlucci provides a necessary and sufficient criterion for characterizing stability of parameterized models. The criterion works for general rational as well as polynomial parameter dependence, unifying previous results. Leveraging this, the author develops an algorithm that enforces stability through convex optimization constraints, eliminating conservatism while allowing greater flexibility in model structure. The method is demonstrated on benchmark examples.

This advance means engineers can build reduced-order models that remain stable over all parameter values without over-constraining the model's behavior. It opens the door to more accurate simulations for design optimization, real-time control, and digital twins in fields like aerospace, automotive, and power systems.