Final answer:
A system can be considered unstable if there is an undefined value in its characteristic equation according to the Routh-Hurwitz criterion. This scenario usually suggests that there are poles with positive real parts, though further analysis would be needed for a definitive conclusion.
Step-by-step explanation:
Can a system be considered unstable in the Routh-Hurwitz criterion if there is an undefined value in its characteristic equation? The answer is Yes.
In the context of the Routh-Hurwitz criterion, an undefined value in a row of the Routh array indicates an unstable system. When constructing the Routh array, every element of the first column is crucial for determining system stability. If an undefined value or a zero exists in this column, special rules must be applied to continue the construction of the Routh array. Even with these adjustments, the presence of an undefined value often signifies a fundamental issue within the system parameters, suggesting that the system may have poles with positive real parts, which in turn denotes instability.
Therefore, encountering an undefined value is an indication that the system has the potential to be unstable. However, a conclusive determination requires further analysis using the Routh-Hurwitz criterion or alternative methods such as the Nyquist plot or root locus technique.