Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599282 | Linear Algebra and its Applications | 2015 | 25 Pages |
Abstract
Let C=A+jB be a complex interval matrix, where A,BâRnÃn are real interval matrices, and j2=â1; denote by D+ the set of positive definite diagonal nÃn matrices. The Schur [respectively Hurwitz] diagonal stability of C, abbreviated as SDS [respectively HDS], is defined in terms of the Stein [respectively Lyapunov] inequality associated with a generic matrix CâC; the inequality must have a common solution QâD+ for all CâC. The paper develops two types of results for the SDS [respectively HDS] analysis, which exploit different properties of C. Each type of results presents (i) a sufficient condition relying on the solvability of a matrix norm inequality (SDS analysis) or a matrix measure inequality (HDS analysis); (ii) a construction procedure for a concrete matrix that satisfies the inequality at (i), and, concomitantly, yields a common solution QâD+. For some particular cases, both necessary and sufficient conditions can be derived. The Schur and Hurwitz approaches are developed in parallel, for concision reasons, as well as for emphasizing the similarities. Numerical examples illustrate the applicability of the theoretical results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Octavian Pastravanu, Mihaela-Hanako Matcovschi,