conditions will allow the true state trajectory to asymptotically converge to the trajectory which gives zero tracking error.        These

stability  conditions are easily     checked  using  Liapunov's indirect method.   It is noted, however, that with Liapunov's approach, the tracking error may only asymptotically converge to zero for a limited range of initial states.     Roughly speaking, this can be considered

equivalent to requiring that the disturbance and reference signals remain small.

     In Chapter Three, using the approach developed for the nonlinear problem, we rederive the well known conditions imposed for a solution to the linear servomechanism problem.

     In Chapter Four, selection of locally stabilizing feedback based on linearization techniques is discussed in detail. Due to the complexity of the stability problem, the control law derived here is for timeinvariant systems which are acted upon by small reference and disturbance signals.    Simulations of a nonlinear system are provided which verify the design technique.    Also discussed in Chapter Four is the interpretation of using optimal control techniques to arrive at the feedback law required for the linear servomechanism problem.        In a

nonlinear system, however, a certain degree of stability is often desired. Consequently, in order to achieve this stability using optimal control theory, a well known technique due to Anderson and Moore [16] is presented.

     In Chapter Five, we develop a controller designed to solve the nonlinear servomechanism   problem  when  a  nominal   input  and  state trajectory are supplied as open-loop commands. Here essentially no new theory is needed since the control problem can actually be treated using