Usually, capital letters (e.g., A, B, F) will denote matrices, while lower case letters (e.g., x, y, z) shall denote vectors.      Both

standard lower case letters and Greek lower case letters shall indicate

a scalar. Any deviations made from the notation for matrices, vectors, and scalars will be clear from context.


          Main Results for the Nonlinear Servomechanism Problem



     Consider the nonlinear system


N:      ;(t) = f(x(t), u(t), w(t))

        y(t) = Hx(t)

        e(t) = r(t) - y(t)                                          (2-2)



where x(t) e Rn is the state of the system, u(t) e RP is the control input to the system, w(t) c Rd is a disturbance signal, y(t) e RP is the output of the system, and e(t) e RP is the error which occurs when

tracking the reference signal r(t) e RP.        Note that the output is

assumed to be a linear function of the state and the dimension of the input is the same as that of the output.

     It is our objective to design a closed-loop controller which will asymptotically regulate against disturbances and also asymptotically

track a reference signal.    In particular, we desire e(t) = r(t) - y(t) + 0 as t + -   where r(t) is a specified output chosen from a given class of functions.

     The primary concern here will be tracking and disturbance rejection when the disturbance w(t) and the reference r(t) are comprised of