IEEE Transactions on Automatic Control, Vol.42, No.4, 564-567, 1997
New Results on the Separation of Matrix Eigenvalues and the Clustering of Matrix-Elements
The problem of separation of matrix eigenvalues is considered in this paper. Necessary and sufficient conditions are given for a matrix to have all eigenvalues contained in an open set defined on the complex plane by a separable polynomial gamma(z(1), z(2)). The problem of clustering of matrix elements is also considered. In this case, a set of matrices is identified, having all eigenvalues in a given subset of the complex plane. The presented results can be useful in both robust stability analysis and the design of control systems.