Automatic Control Systems
If any term in the first column of a Routh array becomes zero, then

Routh criterion can be used by substituting a small negative number for zero and complet-ing the array
Routh criterion can be used by substituting a small positive number for zero and completing the array
Routh criterion can be used by substituting a big positive number for zero and completing the array
Routh criterion cannot be used to determine stability

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Automatic Control Systems
A lag compensator

Speeds up the transient response of the system
Improves steady state behavior of the system
Improves steady state behavior and preserves the transient response of the system
Improves steady state behavior and speeds up the transient response of the system

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