On the Stability of Zero Dynamics of a Single‐Link Flexible Manipulator for a Class of Parametrized Outputs

In order to correct the misinterpretation which has occurred in two recent works concerning the stability of infinite‐dimensional zero dynamics, the stability of zero dynamics of a noncollocated single‐link flexible manipulator is considered in this article for a class of outputs containing a constant parameter. The characteristic equation governing the eigenvalues of zero dynamics is derived. The distribution of these eigenvalues on the complex plane (which depends on the values of the constant parameter) can be found analytically by using the methods of infinite product expansion and root locus. The equivalence of the eigenvalues of zero dynamics and the zeros of the transfer function is also verified.