Errata: In Example 6.8, the state error should be \xi and the input should be F

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Location: page 192, line 4-14

The symbol represents both the system state and the state error, and the symbol should be the input forces . The correct text should read

Letting math and math, the linearized system is given by

math

It can be verified that the system is reachable.

To compute a linear quadratic regulator for the system, we write the cost function as

math

where math and math represent the local coordinates around the desired equilibrium point math. We begin with diagonal matrices for the state and input costs:

math

This gives a control law of the form math, which can then be used to derive the control law in terms of the original variables:

math

As computed in Example 5.4, the equilibrium points have math and math.

(Contributed by C.-H. Choi, 7 Dec 2010)