Laguerre expansion‐based low‐rank balanced truncation for linear switched systems

Abstract This paper proposes a novel Laguerre expansion‐based low‐rank balanced truncation approach for model order reduction of high‐dimensional linear switched systems. First, an iterative procedure is developed to construct low‐rank factors of the infinite reachability and observability Gramians via Laguerre function expansions of matrix exponentials. The reduced‐order model is then obtained using the low‐rank square root method, avoiding the direct solution of large‐scale Lyapunov equations or linear matrix inequalities and thus improving efficiency. Second, an enhanced algorithm integrating dominant subspace projection method is developed, along with a stability preservation theorem that ensures the stability of the reduced‐order models under specific sufficient conditions. Third, the algorithms are applied to systems with coupling or switching matrices, enabling reduction with varying subsystem dimensions while preserving structural compatibility and accurately capturing energy transfer dynamics between modes. Numerical experiments confirm the accuracy and computational efficiency of the proposed algorithms, demonstrating their potential for system analysis and control design.