Abstract :
A novel Khoritonov-like algorithm for computing the minimal and maximal eigenvalues of n*n dimensional symmetric interval matrices is presented. It is proved that the maximal eigenvalue of a given set of interval matrices coincides with the maximal eigenvalue of a special set of 2/sup n-1/ symmetric vertex matrices, whereas its minimal eigenvalue coincides with the minimal of another special set of 2/sup n-1/ symmetric vertex matrices. As immediate corollaries of this algorithm, weak necessary and sufficient conditions for testing the Hurwitz and Schur stability of symmetric interval matrices, where one has to test the stability of 2/sup n-1/ and 2/sup n/ symmetric vertex matrices, respectively, are obtained.<>
Keywords :
eigenvalues and eigenfunctions; matrix algebra; stability; 2/sup n-1/ symmetric vertex matrices; 2/sup n/ symmetric vertex matrices; Hurwitz stability; Khoritonov-like algorithm; Schur stability; extreme eigenvalues; maximal eigenvalues; minimal eigenvalue; real symmetric interval matrices; stability; weak necessary and sufficient conditions; Clustering algorithms; Computational modeling; Eigenvalues and eigenfunctions; Robustness; Stability; Sufficient conditions; Symmetric matrices; Testing;
