Motion Control of Underactuated Mechanical Systems by Javier Moreno-Valenzuela & Carlos Aguilar-Avelar

Author:Javier Moreno-Valenzuela & Carlos Aguilar-Avelar
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

is defined as the disturbance term due to the dynamics neglected by the linearization of , and

(6.49)

In preparation for stating our main results, some properties of the functions in (6.48), in (6.49) and are introduced in the following. The explicit expression of can be obtained from in Appendix B.

Let us define the set

(6.50)

Property 6.1

The function in (6.48) satisfies

(6.51)

where is a positive constant, , and is given in (6.50).

Proof

Using the Mean Value Theorem for and considering the vectors , , and in , one obtains

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