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

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

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Process Control and Instrumentation
Routh test

Criterion is not applicable to systems with polynomial characteristic equation
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
Criterion provides information about the actual location of roots

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