CHEN, W., 2002. On a switching control scheme for nonlinear systems with ill-defined relative degree. Systems & Control Letters, 47(2), pp.159-166.
This paper discusses the applicability of a switching control scheme for a nonlinear
system with ill-defined relative degree. The control scheme switches between exact
and approximate input-output linearisation control laws. Unlike a linear system under
a switching control scheme, the equilibria of a nonlinear system may change
with the switching. It is pointed out that this is not sufficient to cause instability.
When the region of the approximate linearisation control law is attractive to the
exact zero dynamics, it is possible that the closed-loop system under the switching
control scheme is still stable. The results in this paper shows that the switching control
scheme proposed in Tonlin and Sastry (Systems & Control Letters 35(3)(1998)
145-154) is applicable for a wider class of nonlinear systems.