Balancing-based model reduction for switched descriptor systems

Abstract

We propose a novel projection-based model order reduction (MOR) algorithm for a broad class of switched linear descriptor systems. Our approach integrates the reformulation strategy of [Hossain & Trenn, DAE Panel, 2024], which converts the switched descriptor system into a switched ordinary differential equation featuring state- and input-dependent jumps as well as impulsive components at the switching instants in the output, with the piecewise balanced truncation framework for switched linear systems introduced in [Manucci & Unger, arXiv:2601.13039, 2026]. The central idea is to additionally reformulate the switched system with input jumps and impulsive output as a standard switching system that exhibits only state-dependent jumps, while appropriately augmenting the input and output dimensions to preserve the original input-output behavior. Based on this reformulation, we develop new stopping criteria for the stationary iterative scheme employed to approximate the solution of a generalized Lyapunov equation, a key ingredient for the computation of the projection matrices in our MOR procedure. Finally, numerical experiments are conducted to demonstrate and assess the effectiveness of the proposed reduction methodology.