Routh-Hurwitz Criterion in Automatic Control Principles with MATLAB Implementation

This article presents a MATLAB M-language implementation of the Routh-Hurwitz criterion from automatic control principles. We have developed it as a reusable function that can be directly called within control system analysis scripts. The Routh-Hurwitz criterion represents a fundamental concept in control theory for determining system stability through polynomial coefficient analysis. The implementation constructs the Routh array algorithmically by processing the characteristic polynomial coefficients, where each row is computed based on mathematical relationships between previous rows. System stability can only be thoroughly investigated and applied when stability is confirmed, making the Routh-Hurwitz criterion particularly crucial during control system design phases. The function accepts polynomial coefficients as input parameters and returns stability conclusions along with the complete Routh array for analysis. By modifying the input parameters representing different characteristic equations, users can obtain varying stability assessment results, thereby expanding the criterion's application scope to diverse control system configurations. The code includes error handling for special cases such as zero elements in the first column and entire zero rows, ensuring robust performance across various system configurations.