why are the roots of the characteristic equation lying on left half plane of s-plane stable? why not on the right side?

 

In the control systems business there is a saying that "the positive real roots disappear or the system does". Roots in the right half plane correspond to exponential responses that grow to infinity -- essentially destroying the system. Roots in the left half plane correspond to decaying exponentials.

Kind of a basic thing -- don't they teach this stuff any more?