| Interval analysis is widely used in chemical and structural engineering,control circuitry design,robotics,computer graphics,behavioral ecology and other fields.Interval matrices and interval tensors,as the important contents of interval analysis theory,have important applications in the stability of interval dynamical systems.We in this thesis study the localization for eigenvalues of interval matrices and interval tensors,and obtain the localization sets for eigenvalues which are used to study the regularity,positive definiteness and stability of interval matrices and interval tensors.Concretely,We give two new localization sets of eigenvalues of interval matrices.It is proved that the new localization sets are tighter than the existing ones.As applications,the sufficient conditions for the regularity of interval matrices,the sufficient conditions for the positive definiteness of symmetric interval matrices and sufficient conditions for the stability of interval power systems are given;for localizing H-eigenvalues and Zeigenvalues of interval tensors,the localization sets are given to include all Heigenvalues and Z-eigenvalues respectively,which are applied to give the sufficient conditions for the regularity of interval tensor,the positive definiteness of symmetric interval tensor and the stability of a class of nonlinear interval dynamical systems. |
