Process Control and Instrumentation
The Laplace transform of exp(at), where a > 0, is defined only for the Laplace parameter, s > a since

The function exp(at) is piece-wise continuous only for s > a
The Laplace transform integral of exp(at) has initial values only for s > a
The function is exponential
The Laplace transform of integral of exp(at) has finite values only for s > a

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Process Control and Instrumentation
Routh test

Criterion is not applicable to systems with polynomial characteristic equation
Criterion provides information about the actual location of roots
Cannot be used to test the stability of a control system containing transportation lag
Can not determine as to how many roots of the characteristics equation have positive real roots

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