A parametric LTI interpolation for minimum phase systems with guaranteed stability and bounds

Abstract

A stability preserving interpolation method is proposed for parametric SISO LTI systems with a scalar parameter that also guarantees minimum phase property. The parametric SISO LTI system is sampled over a grid of parameter values and the interpolated system is calculated between these samples. The proposed method is based on the geometrical interpolation of the poles and the zeros. The poles and the zeros travel on a particular trajectory while the scalar parameter changes and the samples of these trajectories are known. As the real paths are unknown between samples, artificial trajectories are proposed which are hyperbolic lines. As the main contribution, it is shown that the usage of hyperbolic lines guarantees stability, minimum phase. Furthermore, it guarantees an upper bound on the deviation of the interpolated model from the known models in $H_{\infty}$ sense. An example of a natural frequency optimization problem is presented using the proposed method.