caa a22 4500 467988943 CHVBK 20180323112539.0 cr unu---uuuuu 170328e19901201xx s 000 0 eng 10.1007/BF02551375 doi (NATIONALLICENCE)springer-10.1007/BF02551375 Guardian maps and the generalized stability of parametrized families of matrices and polynomials [Elektronische Daten] [Lahcen Saydy, André Tits, Eyad Abed] 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. Springer-Verlag New York Inc., 1990 Stability nationallicence Robust stability nationallicence Linear systems nationallicence Eigenvalue location nationallicence Polynomial zero location nationallicence Saydy Lahcen Département de Physique, Faculté des Sciences, Université Cadi Ayyad, Marrakech, Morocco aut Tits André the Systems Research Center, University of Maryland, 20742, College Park, Maryland, USA aut Abed Eyad Département de Physique, Faculté des Sciences, Université Cadi Ayyad, Marrakech, Morocco aut Mathematics of Control, Signals and Systems Springer-Verlag 3/4(1990-12-01), 345-371 0932-4194 3:4<345 1990 3 498 https://doi.org/10.1007/BF02551375 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02551375 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Saydy Lahcen Département de Physique, Faculté des Sciences, Université Cadi Ayyad, Marrakech, Morocco aut NATIONALLICENCE 700 1- Tits André the Systems Research Center, University of Maryland, 20742, College Park, Maryland, USA aut NATIONALLICENCE 700 1- Abed Eyad Département de Physique, Faculté des Sciences, Université Cadi Ayyad, Marrakech, Morocco aut NATIONALLICENCE 773 0- Mathematics of Control, Signals and Systems Springer-Verlag 3/4(1990-12-01), 345-371 0932-4194 3:4<345 1990 3 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer