Counterexample and correction to a recent result on robust stability of a diamond of complex polynomials

1991 ◽  
Vol 38 (11) ◽  
pp. 1370-1373 ◽  
Author(s):  
H.I. Kang ◽  
B.R. Barmish ◽  
R. Tempo ◽  
C.V. Hollot
Keyword(s):  
Recent Result ◽  
Robust Stability ◽  
Complex Polynomials

scholarly journals Nonnegativity of uncertain polynomials

1998 ◽  
Vol 4 (2) ◽  
pp. 135-163 ◽  
Author(s):  
Dragoslav D. Šiljak ◽  
Matija D. Šiljak
Keyword(s):  
Robust Stability ◽  
Sufficient Conditions ◽  
Multivariable Systems ◽  
Complex Polynomials ◽  
Matrix Polynomials ◽  
Real Polynomials ◽  
General Parameter ◽  
Positive Realness ◽  
Exclusion Condition ◽  
Parameter Dependent

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.

Robust stability of complex polynomials with annular uncertainties

1994 ◽  
Vol 5 (2) ◽  
pp. 203-215 ◽  
Author(s):  
F. P�rez ◽  
D. Docampo ◽  
C. Abdallah
Keyword(s):  
Robust Stability ◽  
Complex Polynomials
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