Local stabilization of minimum-phase nonlinear systems
After summarizing the definition and computation of the zero dynamics of a nonlinear control system satisfying an invertibility assumption, a system is defined to be minimum phase if the zero dynamics is asymptotically stable. It is observed that minimum phase systems can be easily made asymptotically stable by feedback assuming that the \(m\times m\) matrix with (i,j)-th element \(<dh_ i,g_ j>\), with \(h_ i\) the i- th output function and \(g_ j\) the j-th input vectorfield, has rank m. If this assumption is not satisfied then it is shown that new output functions can be constructed for which the assumption holds and the minimum phase property is preserved, thereby yielding as before a stabilizing feedback.
scientific article; zbMATH DE number 4061084
scientific article