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We consider the reduction of parametric families of linear dynamical systemshaving an affine parameter dependence that differ from one another by alow-rank variation in the state matrix. Usual approaches for parametric modelreduction typically involve exploring the parameter space to isolaterepresentative models on which to focus model reduction methodology, which arethen combined in various ways in order to interpolate the response from theserepresentative models. The initial exploration of the parameter space can be aforbiddingly expensive task. A different approach is proposed here that doesnot require any parameter sampling or exploration of the parameter space.Instead, we represent the system response in terms of four subsystems that arenonparametric. One may apply any one of a number of standard (nonparametric)model reduction strategies to reduce the subsystems independently, and thenconjoin these reduced models with the underlying parameterized representationto obtain an overall parameterized response. Our approach has elements incommon with the parameter mapping approach of Baur et al. [8], but offersgreater flexibility and potentially greater control over accuracy. Inparticular, a data-driven variation of our approach is described that exercisesthis flexibility through the use of limited frequency-sampling of theunderlying nonparametric models. The parametric structure of our systemrepresentation allows for a priori guarantees of system stability the resultingparametric reduced models, uniformly across all parameter values. Incorporationof system theoretic error bounds allow us to determine appropriateapproximation orders for the nonparametric systems sufficient to yielduniformly high accuracy with respect to parameter variation.

Sampling-free parametric model reduction for structured systems