Model Reduction for Aperiodically Sampled Data Systems

TL;DR

This paper presents two moment matching-based model reduction methods for aperiodically sampled data systems, represented as linear switched state space models, ensuring stability preservation and comparing their effectiveness through numerical examples.

Contribution

It introduces two novel approaches for model reduction of aperiodically sampled systems using moment matching, with stability guarantees and comparative analysis.

Findings

Both methods preserve quadratic stability for stable plants.

Numerical examples demonstrate the effectiveness of the proposed approaches.

Comparison shows trade-offs between the two reduction strategies.

Abstract

Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its value from a pre-specified finite set of allowed sampling intervals. Such systems can be represented by discrete-time linear switched (LS) state space (SS) models. One of the approaches investigated in the paper is to apply model reduction by moment matching on the linear time-invariant (LTI) plant model, then compare the responses of the LS SS models acquired from the original and reduced order LTI plants. The second approach is to apply a moment matching based model reduction method on the LS SS model acquired from the original LTI plant, and then compare the responses of the original and reduced LS SS models. It is proven that for both methods, as long as the original LTI plant is stable, the resulting reduced order LS SS model of the sampled data system is quadratically stable. The results from two approaches are compared with numerical examples.