Errata: In Example 4.6, u d is not computed correctly

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Location: page 107, line 12--15

In Example 4.6, on the design of a state feedback controller for the compartment model, the computation for u_d is not correct. The form of the feedback law is u = k(y − y_d) + u_d but the feedback law substituted into the dynamics is missing the y_d term. To fix this, the equation on line 12 should be modified to read

The equilibrium concentration is then given by x_e = − A ^{− 1}Bu_e and the equilibrium output has the form

This equation can then be solved for u_d as a function of the desired output by setting y_e = y_d.

(Contributed by F. Zabala, 10 Oct 09)