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

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