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single-input single-output systems. As expected, the resulting
controller requires integrators in the feedback loop.
Solomon and Davison [13] have used state-space techniques to treat
the servomechanism problem for a certain class on nonlinear systems.
They too have considered only constant reference and disturbance
signals. In addition, the nature of the disturbance is such that it
affects the output directly without affecting the dynamics of the
nonlinear system. It can be shown that such a disturbance can be
regarded as simply a change in the level of the reference signal.
Various assumptions are made and conditions are given stating when it is
possible to solve this servomechanism problem. The resulting control
law employs integrators in the feedback loop and nonlinear feedback is
used to give global stability. Although global stability is obtained,
the range in amplitude of the reference and disturbance signals which
can be applied is limited.
Some appealing results, again only for the case of constant
reference and disturbance signals, are derived in Desoer ad Lin [14] and
in Anantharam and Desoer [15]. Desoer and Lin have shown that if the
nonlinear plant has been prestabilized so that it is exponentially
stable and if the stabilized plant has a strictly increasing, dc,
steady-state, input-output map then the servomechanism can be solved
with a simple proportional plus integral controller. Using such a
control scheme, it is necessary that the gains of the integrators be
sufficiently small and that the proportional gain be chosen
appropriately. Anantharam and Desoer have derived results virtually
identical to those found in Desoer and Lin. In their paper, however,
the proof is somewhat different and a nonlinear discrete-time system is