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

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Process Control and Instrumentation
For a feed back control system to be stable, the

Bode plots of the corresponding open loop transfer function should monotoni-cally decrease
Poles of the closed loop transfer function should lie in the left half of the complex plane
Roots of the characteristic equation should be real
Poles of the closed loop transfer function should lie in the right half of the complex plane

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