46
This means that x is also an eigenvalue of the matrix
F GKX -GK2
-BH A
Since the system LCT can be written as
*(t)~
F GKj
-gk2
~x(t)~
Ti(t)_
-BH
A
jn(t)_
and x is, by assumption, in the closed right half-plane then LCT is not
asymptotically stable. This is a contradiction to the assertion that
LCT is asymptotically stable and the proof is complete.
Theorems 3.2, 3.3, and 3.4 show that when conditions (B.l) and
(B.2) are true, then all requirements for a solution to the linear
servomechanism problem are satisfied. Furthermore, this has been
accomplished in the framework developed for the nonlinear servomechanism
problem. In the next chapter, we shall apply some of these results to
obtaining the stability required for the nonlinear servomechansim
problem using the linearization approach.