A tool leveraging the Routh-Hurwitz stability criterion determines the stability of a linear, time-invariant (LTI) system. This mathematical method assesses stability by analyzing the characteristic polynomial of the system’s transfer function, without requiring explicit calculation of the system’s roots. Typically, this analysis involves constructing a special table, known as the Routh array, from the polynomial’s coefficients. The array’s entries provide insight into the location of the system’s poles in the complex plane, indicating whether the system is stable, marginally stable, or unstable.
This analytical method offers significant advantages in control systems engineering and other fields involving dynamic systems. It provides a quick and efficient way to assess stability without complex computations, allowing engineers to design and analyze systems with greater confidence. Developed in the late 19th century, this method remains a fundamental tool for stability analysis due to its simplicity and effectiveness. It avoids the often computationally intensive task of finding polynomial roots, making it particularly useful for higher-order systems.
