# 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 and , the linearized system is given by

It can be verified that the system is reachable.

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

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

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

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

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