Robust Stability of Complex Families of Matrices and Polynomials
Recently, the authors introduced the “guardian map” approach as a unifying tool in the study of robust generalized stability questions for parametrized families of matrices and polynomials. Real matrices and polynomials have been emphasized in previous reports on this approach. In the present note, the approach is discussed in the context of complex matrices and polynomials In the case of polynomials, some algebraic connections with other recent work are uncovered.
KeywordsParametrized Family Complex Matrice Robust Stability Real Matrice Monic Polynomial
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- L. Saydy, A.L. Tits and E.H. Abed, “Guardian Maps and the Generalized Stability of Parametrized Families of Matrices and Polynomials,” Mathematics of Control, Signals and Systems 3 (1990, in press).Google Scholar
- N.K. Bose, “Tests for Hurwitz and Schur Properties of Convex Combination of Complex Polynomials,” IEEE Trans. Circuits and Syst. CAS-36 (1989), 1245–1247.Google Scholar
- N. K. Bose and Y. Q. Shi, “Network Realizability Theory Approach to Stability of Complex Polynomials,” IEEE Trans. Circuits and Systems CAS-34 (1987), 216–218.Google Scholar
- A. Rantzer, “An Efficient Test for the Stability of Families of Polynomials,” in Realization and Modeling in System Theory. Proceedings of the International Symposium MTNS-89 — Volume 2, M.A. Kaashoek, J.H. van Schuppen and A.C.M. Ran, eds., Birkhäuser, New York, 1990.Google Scholar
- L. Saydy, A.L. Tits and E.H. Abed, “Robust Stability of Linear Systems Relative to Guarded Domains,” Proc. 27th IEEE Conf. on Decision and Control, Austin, Texas (December 1988).Google Scholar
- P. Lancaster and M. Tismenetsky, The Theory of Matrices, Academic Press, New York, 1985.Google Scholar
- C. Stéphanos, “Sur une Extension du Calcul des Substitutions Linéaires,” J. Math. Pures Appl. 6 (1900), 73–128.Google Scholar
- S. Bialas, “A Necessary and Sufficient Condition for the Stability of Convex Combinations of Polynomials or Matrices,” Bulletin of the Polish Academy of Sciences 33 (1985), 473–480.Google Scholar
- J.E. Ackermann and B.R. Barmish, IEEE Trans. Automat. Control AC-33 (1988), 984–986.Google Scholar