Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498394 | Linear Algebra and its Applications | 2005 | 20 Pages |
Abstract
This paper investigates necessary and sufficient conditions for the existence of an affine parameter-dependent Lyapunov function assuring the Hurwitz (or Schur) stability of a polytope of matrices. A systematic procedure for constructing a family of linear matrix inequalities conditions of increasing precision is given. At each step, a set of linear matrix inequalities provides sufficient conditions for the existence of the affine parameter-dependent Lyapunov function. Necessity is asymptotically attained through a relaxation based on a generalization of Pólya's Theorem to the case of matrix valued functions. Numerical experiments illustrate the results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ricardo C.L.F. Oliveira, Pedro L.D. Peres,