On Stability of Parametrized Families of Polynomials and Matrices
The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices 𝒜 is equivalent to the nonsingularity of the family {𝐴2−2...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/687951 |
| Summary: | The Schur and Hurwitz stability problems for a parametric polynomial
family as well as the Schur stability problem for a compact set of real
matrix family are considered. It is established that the Schur stability
of a family of real matrices 𝒜 is equivalent to the nonsingularity
of the family {𝐴2−2𝑡𝐴+𝐼∶𝐴∈𝒜,𝑡∈[−1,1]} if 𝒜 has at
least one stable member. Based on the Bernstein expansion of a
multivariable polynomial and extremal properties of a multilinear
function, fast algorithms are suggested. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |