Generation of robust root loci for linear systems with parametric uncertainties in an ellipsoid |
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Authors: | Shih-Feng Yang Chyi Hwang |
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Affiliation: | CESAME , Université Catholique de Louvain , 4-6 avenue G. Lema?tre 1348, Louvain-la-Neuve, Belgium E-mail: dochain@csam.ucl.ac.be |
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Abstract: | Given a parametric polynomial family p(s; Q) := {n k=0 ak (q)sk : q ] Q}, Q R m , the robust root locus of p(s; Q) is defined as the two-dimensional zero set p,Q := {s ] C:p(s; q) = 0 for some q ] Q}. In this paper we are concerned with the problem of generating robust root loci for the parametric polynomial family p(s; E) whose polynomial coefficients depend polynomially on elements of the parameter vector q ] E which lies in an m-dimensional ellipsoid E. More precisely, we present a computational technique for testing the zero inclusion/exclusion of the value set p(z; E) for a fixed point z in C, and then apply an integer-labelled pivoting procedure to generate the boundary of each subregion of the robust root locus p,E . The proposed zero inclusion/exclusion test algorithm is based on using some simple sufficient conditions for the zero inclusion and exclusion of the value set p(z,E) and subdividing the domain E iteratively. Furthermore, an interval method is incorporated in the algorithm to speed up the process of zero inclusion/exclusion test by reducing the number of zero inclusion test operations. To illustrate the effectiveness of the proposed algorithm for the generation of robust root locus, an example is provided. |
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