closed-loop transient system. Again, the approach taken here is seen to be drastically different from the approach taken in the well known linear servomechanism problem. Asymptotic stability of the closed-loop transient system was allowed to be either global or local; however, with local stability it was indicated that tracking and disturbance rejection would occur only for certain initial states. These initial states were
restricted to the neighborhood of the particular initial state which defined the equilibrium point of the closed-loop transient system.
The dynamic equations modeling the closed-loop transient system were seen to be nonlinear and somewhat complicated. In order to apply Liaponov's indirect method, a much simpler dynamic system was derived
through linearizations. Although the linearized model is much more suitable for feedback gain selection, stability of the linearized model only insures local stability of the true system.
In this chapter, no discussion was given as to possible means of determining the stabilizing feedback gains. This topic is the subject of Chapters Four and Five.