We provide an alternative solution to the problem of semi‐global stabilization of a class of minimum phase nonlinear systems which is considered in Reference 17. Our method yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed in Reference 17. We eliminate the peaking phenomenon by inducing a specific time‐scale structure in the linear part of the closed‐loop system. This time‐scale structure consists of a very slow and a very fast time scale. The crucial component in our method is the relation between the slow and the fast time scales. Our proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set.
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Lin et al. (1994) studied this question.