Errata: In Example 9.6, the critical gain is k = 0.5 instead of k = 1

Location: page 276, lines -6, -2; page 277, line 4

In Example 9.6, the value of the critical gain is listed incorrectly: it should be $\text{[math]}$ instead of $\text{[math]}$ . The paragraph after the displayed equation has several changes (highlighted in blue):

We have $\text{[math]}$ and $\text{[math]}$ . If $\text{[math]}$ , the Nyquist curve encircles the critical point $\text{[math]}$ in the counterclockwise direction when the Nyquist contour $\text{[math]}$ is encircled in the clockwise direction. The number of encirclements is thus $\text{[math]}$ . Since the loop transfer function has one pole in the right half-plane ( $\text{[math]}$ ), we find that $\text{[math]}$ and the system is thus stable for $\text{[math]}$ . If $\text{[math]}$ , there is no encirclement and the closed loop will have one pole in the right half-plane.