OK, there two definitions of pole.
For example, H=1/(s+2):
1st definition, the denominator is 0, s+2=0, s=-2, which makes H to be infinite, now the pole frequency is a negative value at the complex plane, a negative pole makes the system stable.
2nd definition, the gain drops to -3dB of the H, which means s=2, a positive frequency on the frequency domain, so this pole, unlike the 1st definiton pole, makes the gain H to drops to H/2 (3dB).
Then for the 1st definition of pole, which is on the left plane, with a negative value, while it is positive on the frequency domain in the 2nd definition. right? Thanks.
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A positive pole in the 2nd definition, for example, changing its sign, it becomes to a negative pole in the 1st definition at the s plane, which is easy to transfer to the exponential part presenting as a time domain signal to analysis.