Separation of eigenvalues and applications to systems theory

This thesis presents a method for the separation of eigenvalues of a system matrix relative to rectangles, circles, or sectors in either the X-plane for continuous-time systems or the z-plane for discrete-time systems. Also, it is concerned with the block diagonalization and the block- triangularization of a system matrix into various submatrices which contain the eigenvalues of the system matrix lying within specified domains in a complex plane. The generalized matrix sign function of a system map in a matrix bilinear form is used for the development. The proposed methods are suitable for the analysis and design of large-scale continuous-time and discrete-time systems having multiple time scale structures.