Robust Stability of Multivariate Polynomials, Part 2: Polytopic Coefficient Variations

Multidimensional Systems and Signal Processing

Volumn 10, Issue 1, 1999, Pages 21-32

  Kharitonov, V L ^a   Torres Munoz J A ^a   Ramirez Sosa M I ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Multivariate polynomials; Polytopic families; Robust stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; POLYNOMIALS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

HUWIRTZ STABLE POLYNOMIALS; MULTIVARIATE POLYNOMIALS;

MULTIVARIABLE CONTROL SYSTEMS;

EID: 0032663266     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008437801340     Document Type: Article

References (12)

1. Kharitonov, V.L. and Torres-Muñoz, J. A. (1998). Robust Stability of Multivariate Polynomials Part 1: small coefficient perturbations. Multidimensional Systems and Signal Processing, in press.
2. Bose, N.K. (1988). Robust multivariable scattering Hurwitz interval polynomial. Linear Algebra and Its Applications, 98:123-136.
3. Basu, S. (1989). On the Multidimensional Generalization of Robustness of Scattering Hurwitz Property of Complex Polynomials. IEEE Trans. on Circuits and Systems, 36:1159-1167.
4. Kogan, J. (1993). Computation of stability radius for families of bivariate polynomials. Multidimensional Systems and Signal Processing, 4:151-165.
5. Polyak, B.T. and Shmulyian, S.B. (1994). Frequency Domain Criteria for Robust Stability of Bivariate Polynomials. IEEE Trans, on Circuits and Systems-1: Fundamental Theory and Applications, 41:161-167.
6. Bose, N.K. (1996). Edge property from end-points for scattering Hurwitz polynomials. Automatica, 32:655-657.
7. Basu, S. (1990). On boundary implications of stability and positivity properties of multidimensional systems. Proceedings of IEEE, 78:614-626.
8. Barmish, B.R., Tempo, R., Hollot, C.V. and Kang, H.I. (1992). An extreme point result for robust stability of a diamond of polynomials. IEEE Trans, on Automatic Control, AC-37:1460-1462.
9. Bartlett, A.C., Hollot, C.V. and Huang, L. (1988). Root locations of an entire polytope of polynomials: It suffices to check the edges. Mathematics of Control, Signals and Systems, 1:61-71.
10. Rantzer, A. (1992). Stability conditions for polytopes of polynomials. IEEE Trans, on Automatic Control, AC-37:79-89.
11. Kharitonov, V.L. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial'nye Uravneniya, 14:2086-2088.
12. Tempo, R. (1990). A dual result to Kharitonov's theorem. IEEE Trans, on Automatic Control, AC-35:195-198.