A comparative study on balanced truncation and projection onto the dominant eigenspace of the Gramian using Laguerre functions

This paper presents a comparative analysis of two model reduction techniques: balanced truncation and projection onto the dominant eigenspace of the Gramian. Both methods are evaluated through the lens of Laguerre functions which is a reduction technique based on Laguerre function expansion, that approximates the low-rank factors of the Controllability and Observability Gramians to produce approximately balanced systems without solving Lyapunov equations. We demonstrate the effectiveness of each approach in reducing the complexity of linear time-invariant (LTI) systems while preserving system dynamics. Numerical experiments highlight the strengths and weaknesses of both methods, showcasing their applicability to large-scale systems. By thoroughly analyzing both methods in conjunction with Laguerre functions, we contribute to the ongoing discourse in the field and lay the groundwork for future advancements in model reduction techniques.