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

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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 instead of . The paragraph after the displayed equation has several changes (highlighted in blue):

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

In addition, in the caption of Figure 9.8, the Nyquist plot is given for gain .

(Contributed by F. Zabala, 23 Dec 09)