On pole and zero sensitivity of linear systems

The pole and zero sensitivity with respect to a realization of linear systems is investigated. It is shown that the pole and zero sensitivity measure depend strongly upon the realization chosen. The set of optimal similarity transformations that convert any realization into an optimal one is completely characterized in terms of minimizing pole and zero sensitivity measure, respectively. The pole and zero sensitivity simultaneous minimization problem is considered. The necessary and sufficient condition is given for the optimal zero sensitivity realizations with minimal pole sensitivity. An iterative algorithm is proposed to find the optimal realizations. A numerical example is given which confirms the theoretical results.