The proof uses a back-stepping procedure and an inductive argument. Thus, under the assumptions (i), (ii) and (iv), a global change of coordinates for the system exists such that the system is in the strict-feedback form [140, 153, 199, 212]. By augmenting the ρ linearly independent set
with an arbitrary n−ρ linearly independent set zρ+1 = ψρ+1(x),…, zn = ψn with ψi(0) = 0, 〈dψi, Gρ−1〉 = 0, ρ + 1 ≤ i ≤ n. Then the state feedback
globally transforms the system into the form:
(A.1) |
where zμ = (zρ+1,…, zn). Moreover, in the z-coordinates we have
so ...
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