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5.2 Feedback-Linearization Controllers 269

(5.2.14)

It may then be shown using Theorem 2.11.5 that this system is SPR if

(5.2.15)

with the choice of

(5.2.16)

such that

(5.2.17)

is the positive-definite solution to the Lyapunov equation

(5.2.18)

and

(5.2.19)

The next theorem presents sufficient conditions for the uniform boundedness
of the trajectory error.

THEOREM 5.2–1: The closed-loop system given by (5.2.13) will be uniformly
bounded if

and

where K v=2aI and K p=4aI.

Proof:

Copyright © 2004 by Marcel Dekker, Inc.