Final answer:
The necessary and sufficient condition for stability in a feedback system is that all the poles of the system transfer function have negative real parts.
Step-by-step explanation:
The statement that all the poles of the system transfer function must have positive real parts in order for a feedback system to be stable is False. The necessary and sufficient condition for stability in a feedback system is that all the poles of the system transfer function have negative real parts.
A pole is a value of the frequency response where the denominator of the transfer function becomes zero. The real part of a pole determines the stability of the system. If the real part is positive, the system is unstable, and if the real part is negative, the system is stable.
For example, consider a simple feedback system with a transfer function H(s) = 1 / (s + 1). The pole of this system is -1, which has a negative real part, indicating stability.