(t)
TA=T*(t)
*
w=w (t)
-1 _*
J 1(e )
(6-13)
It is not difficult [24] to derive equations which explicitly relate the
matrices Fj(t) and ^(t) to the nominal trajectory, however, in the
interest of brevity, we omit these derivations.
Now consider the feasibility of selecting the feedback gains to
stabilize the linearized closed-loop system. Assuming that the slowly
time-varying approach will apply, the eigenvalues of the linearized
matrix must lie in the open left half-plane for all t. Theorem 3.3 can
be used to determine when it is possible to meet this goal using an
appropriate feedback law. Interpreting Theorem 3.3 for the slowly time-
varying system, the following conditions must hold:
(1) [Fx(t), G,(t)] must be controllable at each t.
0
must have full rank (rank 3N) for
each t and for each which is an eigenvalue of the internal model
matrix A.