The control system is stable if all of the roots of the characteristic equation can be found in the left half of the's' plane.
The control system is unstable if at least one characteristic equation root is located in the right-half of the "s" plane. This standard only applies to linear systems. The exact locations of the poles on the right and left halves of the S plane are not given. The characteristic equation can only be used with real coefficients. The characteristic polynomial's coefficients must be positive in order for the condition to exist. This suggests that there should be negative real parts in all of the characteristic equation's roots.
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