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 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
The function is exponential

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Process Control and Instrumentation
The characteristic equation for the control system with a closed loop transfer function G₁/1 + Gā‚‚ is given by 1 + Gā‚‚ = 0. The characteristic equation for the control system

Determines its stability
Is the same for set point or load changes
All of these
Depends only upon the open loop transfer function

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