论文信息 - Conservatism of the circle criterion-solution of a problem posed by A. Megretski

Conservatism of the circle criterion-solution of a problem posed by A. Megretski

In the collection of open problems in mathematical systems and control theory Blondel et al. (1999), Megretski poses a problem related to the degree of conservativism of the well-known circle criterion follows. We solve this problem.

Siegfried M. Rump | S. Rump

[1] Charles R. Johnson,et al. Convex sets of nonsingular and P:–Matrices , 1995 .

[2] A. Megretski. How conservative is the circle criterion , 1999 .

[3] Arjan van der Schaft,et al. Open Problems in Mathematical Systems and Control Theory , 1999 .

[4] Nicholas J. Higham,et al. INVERSE PROBLEMS NEWSLETTER , 1991 .

[5] J. Rohn. Systems of linear interval equations , 1989 .

[6] M. Fiedler. Special matrices and their applications in numerical mathematics , 1986 .

[7] S. Rump. THEOREMS OF PERRON-FROBENIUS TYPE FOR MATRICES WITHOUT SIGN RESTRICTIONS , 1997 .

[8] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[9] James Demmel,et al. The Componentwise Distance to the Nearest Singular Matrix , 1992, SIAM J. Matrix Anal. Appl..

[10] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[11] Andrew Packard,et al. The complex structured singular value , 1993, Autom..

[12] Siegfried M. Rump. Ill-Conditioned Matrices Are Componentwise Near to Singularity , 1999, SIAM Rev..