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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
Guardian maps and the generalized stability of parametrized families of matrices and polynomials
Mathematics of Control, Signals, and Systems, Volume 3, No. 4, Year 1990
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Description
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 prescribed 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. 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. © 1990 Springer-Verlag New York Inc.
Authors & Co-Authors
Saydy, Lahcen
Morocco, Marakech
Université Cadi Ayyad
Tits, André L.
United States, College Park
University of Maryland, College Park
Sweden, Lund
Lunds Tekniska Högskola
Abed, Eyad H.
Morocco, Marakech
Université Cadi Ayyad
Sweden, Lund
Lunds Tekniska Högskola
Statistics
Citations: 156
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1007/BF02551375
ISSN:
09324194
e-ISSN:
1435568X