Routh-Hurwitz Criterion, Special Cases

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This video presents two special cases that you can encounter when filling out the Routh Array. The first case is when there is a zero in a row with at least one non-zero element following it, and the second case is when there is an entire row of zeros. I explain how to continue filling out the Routh Array for each of these cases and provide a little insight into what they mean for the system stability.
I will be loading a new video each week and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!
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In the first example you give, the one which you didn't go over and had the first row 1 0 4, I don't see why the zero here would cause an issue with calculation that would require one to replace it with epsilon. The second example makes send, but as far as I can tell the only time you need to use the epsilon method is when the zero appears as the first number in a row followed by non-zero numbers since it would lead to division by zero.

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Nice video but there is a small mistake in special case 1. If the elements above and below the ε in the first column have the same sign, a pair of imaginary roots is indicated, which means the system is marginally stable (e.g s^3+2s^2+s+2)

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[@shipak13579]

This is nice, but regarding epsilon, and zero in a row, I think that system can be marginal stable if there is no sign change when epsilon tends to 0+, you mentioned it is always unstable (at 11:45). Correct me if I am wrong. Best regards.