Nonnegativity of uncertain polynomials

Mathematical Problems in Engineering

Dragoslav D. Šiljak¹  Matija D. Šiljak² 

[1] Department of Electrical Engineering, Santa Clara University, Santa Clara, CA 95053, USA;Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA;

关键词: Interval polynomials;    uncertain parameters;    polytope families;    matrix polynomials;    absolute stability.;   

DOI  :  10.1155/S1024123X98000763

来源: DOAJ

【 摘 要 】

The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

【 授权许可】

Unknown