only state feedback with constant gain matrices can be used to achieve this stability. The system NCT is given again here for convenience.
NCT:
X(t) = f(x*(t)+W(t), u (t)+w(t), w*(t)) - f(x*(t), u*(t), w*(t)) "'( t) = An(t) - BH"X(t)
'i'( t) -Kl (tM - K2 rt (4-1)
Two forms of asymptotic stability are actually considered in the
solution to the servomechanism problem: global stability and local
stability. It was indicated that local stability allows tracking and disturbance rejection to occur only for certain initial states whereas global stability allows tracking and disturbance rejection for all initial states. Global stability is thus the most desirable form of
stability, however, due to the diversity which can occur in the system NCT, we shall limit our concern to the local stability problem. In
addition, the original nonlinear plant will be taken as time-invariant (i.e., the function f(x,u,w) is independent of time). These
restrictions will allow us to obtain a time-invariant feedback law which
gives local tracking and disturbance rejection for small reference and disturbance signals.
For convenience, when discussing the system NCT, the following definition shall be used
t : (t
×A~t : L(t!(4-2)