RH-Criteria

The Routh-Hurwitz criteria in control systems is a mathematical method used to determine the stability of a system by analyzing the coefficients of its characteristic polynomial. By constructing a table known as the Routh array using the coefficients of the polynomial, the criteria can determine the number of roots of the characteristic equation that lie in the right-half of the complex plane.

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Description

The Routh array provides a systematic way to check for stability without solving for the roots directly. According to the criteria, a system is stable if and only if all the elements in the first column of the Routh array have the same sign, and there are no sign changes in the first column. If any sign changes occur, the system may have unstable poles. The Routh-Hurwitz criteria offer a powerful tool for engineers to analyze and design stable control systems, particularly in situations where root locus or frequency domain methods are not applicable.