Guardian Maps and the Generalized Stability of Parametrized Families of Matrices and Polynomials
Abstract
The generalized stability of families of real matrices and polynomials is considered. (Generalized stability is meant in the usual sense of confinement of matrix eigenvalues or polynomial zeros to a prespecified domain in the complex plane, and includes Hurwitz and Schur stability as special cases.) "Guardian maps" and "semiguardian maps" are introduced as a unifying tool for the study of this problem. Basically these are scalar maps which vanish when their matrix or polynomial argument loses stability. Such maps are exhibited for a wide variety of cases of interest corresponding to generalized stability with respect to domains of the complex plane. In the case of one- and two-parameter families of matrices or polynomials, concise necessary and sufficient conditions for generalized stability are derived. For the general multiparameter case, the problem is transformed into one of checking that a given map is nonzero for the allowed parameter values.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1989
- Accession Number
- ADA454727
Entities
People
- Andre Tits
- Eyad H. Abed
- Lahcen Saydy
Organizations
- University of Maryland