Robust stability of a class of polynomials with coefficients depending multilinearly on perturbations

Necessary and sufficient conditions are given for robust stability of a family of polynomials. Each polynomial is obtained by a multilinearity perturbation structure. Restrictions on the multilinearity are involved, but, in contrast to existing literature, these restrictions are derived from physical considerations stemming from analysis of a closed-loop interval feedback system. The main result indicates that all polynomials in the family of polynomials have their zeros in the strict left half-plane if and only if two requirements are satisfied at each frequency. The first requirement is the zero exclusion condition involving four Kharitonov rectangles. The second requirement is that a specially constructed theta 0-parameterized set of 16 intervals must cover the positive reals for each theta epsilon (0,2 pi ). >

[1]  Douglas Looze,et al.  Unmodeled dynamics: Performance and stability via parameter space methods , 1987, 26th IEEE Conference on Decision and Control.

[2]  Shaping conditions for the robust stability of polynomials with multilinear parameter uncertainty , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[3]  André L. Tits,et al.  On the robust stability of polynomials with no cross-coupling between the perturbations in the coefficients of even odd powers , 1989 .

[4]  C. Desoer,et al.  Linear System Theory , 1963 .

[5]  B. Barmish.  A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations , 1988, 1988 American Control Conference.

[6]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[7]  M. Saeki.  Method of robust stability analysis with highly structured uncertainties , 1986 .

[8]  Athanasios Sideris,et al.  Multivariable stability margin calculation with uncertain correlated parameters , 1986, 1986 25th IEEE Conference on Decision and Control.

[9]  B. Barmish.  New tools for robustness analysis , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[10]  Parameter Partitioning via Shaping Conditions for the Stability of Families of Polynomials , 1989, 1988 American Control Conference.

[11]  C. Desoer,et al.  An elementary proof of Kharitonov's stability theorem with extensions , 1989 .

[12]  S. Dasgupta.  Kharitonov's theorem revisited , 1988 .