This means that x is also an eigenvalue of the matrix
F- GK 1 -GK21
LF-BH Aj
Since the system LCT can be written as
t = - GK1 -GK2 (t1 (3-21)
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.1) 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.