The General Solution for Affine Control Systems on Lie Groups

The General Solution for Affine Control Systems on Lie Groups

“…Our first purpose is to study the solution of Σ. To construct the solution (see Theorem 2.4) we use a technique developed in [4] and improved in [9] (see Section 2 for more details). In particular, considering R n as Lie group it is not difficult to see that our solution is an extension of that one presented in [1, ch.3].…”

“…Under the above assumptions, if F : G → H is a homomorphism of Lie groups, then a necessary and sufficient condition for affine systems(9) and (10) to be conjugate is dF e e Dt Z j = e D ′ t W j , for all j = 1, . .…”