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RH Criteria | Solved Problem-1 | Control System


The Routh-Hurwitz Criterion is a powerful tool in control system theory that helps us determine whether a system is stable without solving for the roots of its characteristic equation. Stability here means that the system's output remains bounded over time.

The process involves:

1. Writing the characteristic equation of the system.

2. Constructing the Routh Array using the coefficients of the equation.

3. Checking the signs of the first column in the Routh Array:

4. If all elements in the first column have the same sign, the system is stable.

If there are sign changes, the number of changes corresponds to the number of roots with positive real parts, indicating instability.

This method is widely used because it simplifies stability analysis, especially for higher-order systems, without requiring complex root calculations.


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