Stability Analysis of Linear Systems Using the Routh-Hurwitz Criterion: Theory and Applications

Abstract

Stability is a crucial factor in ensuring the reliable operation of linear systems, especially in fields like control engineering, signal processing, and mechanical design. This paper provides an in-depth look at the Routh-Hurwitz Criterion, an algebraic method that enables stability analysis without the need for direct calculation of eigenvalues. By constructing a Routh array from the system’s characteristic polynomial, we can assess stability through a straightforward inspection of coefficient patterns. We explore the theoretical basis of the Routh-Hurwitz Criterion and tackle some common challenges, such as dealing with zeros in critical positions within the array. Real-world applications demonstrate the criterion’s effectiveness in fields ranging from feedback control to oscillatory systems, showcasing how this approach offers both efficiency and insight. This work serves as a practical guide for researchers and engineers who seek a robust, accessible tool for analyzing the stability of linear systems.