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On the stability of large matrices

✍ Scribed by A.N. MalysheV; M. Sadkane

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
667 KB
Volume
102
Category
Article
ISSN
0377-0427

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✦ Synopsis

The distance rstab(d) of a stable matrix A to the set of unstable matrices and the norm of the exponential of matrices constitute two important topics in stability theory. We treat in this note the case of large matrices. The method proposed partitions the matrix into two blocks: a small block in which the stability is studied and a large block whose field of values is located in the complex plane. Using the information on the blocks and some results on perturbation theory, we give sufficient conditions for the stability of the original matrix, a lower bound of rstab(A) and an upper bound on the norm of the exponential of A. We illustrate these theoretical bounds on a practical test problem.

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