A general theory for analysis and design of robust pole clustering in subregions of the complex plane

This paper presents a general theory for analysis and design of robust pole clustering in a very general subregion Ω of the complex plane for uncertain systems with unstructured or structured uncertainties. The pole clustering regions of interest cover any Ω-transformable and non-Ω-transformable Ω-regions which are broader than those reported in the literature. Discussions regarding robust D-stability (robust pole clustering) and quadratic D-stability (quadratic pole clustering) are presented. Based on the Rayleigh principle, three new approaches are developed for analysis of robust pole clustering in a general subregion Ω of the complex plane. By applying these analysis results, an output-feedback robust D-stability design method is developed for a general regional-pole placement of uncertain systems.