Interconnection-based Model Reduction for Linear Hybrid Systems

TL;DR

This paper develops a novel model reduction technique for linear hybrid systems using interconnection-based moment matching, enabling efficient approximation of system behavior while handling hybrid dynamics.

Contribution

It introduces a hybrid characterization for moment matching in linear hybrid systems and designs reduced models that match moments for multiple interconnections simultaneously.

Findings

Reduced-order models achieve accurate steady-state response approximation.

The method simplifies for systems with periodic jumps.

Numerical simulations validate the effectiveness of the approach.

Abstract

In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in the hybrid setting, and we present families of reduced-order models for each interconnection via a hybrid characterisation of the steady-state responses. By combining the results for each interconnection, the design of a reduced-order model that achieves moment matching simultaneously for both interconnections is studied. In addition, we show that the presented results have simplified counterparts when the jumps of the hybrid system are periodic. A numerical simulation is finally given to illustrate the results.