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Which of the following is $\text{NOT}$ a necessary condition for a process under closed-loop control to be stable?

- Dead-time term(s) must be absent in the open-loop transfer function
- Roots of the characteristic equation must have negative real part
- All the elements in the left (first) column of the Routh array must have the same sign
- Open-loop transfer function must have an amplitude ratio less than $1$ at the critical frequency