Computation of the stability radius of a Hurwitz polynomial with diamond-like uncertainties

✍ Scribed by Q.-H. Wu

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 182 KB
• Volume: 35
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(98)00028-0

✦ Synopsis

This paper considers the stability radius problem of Hurwitz polynomials whose coe cients have H older 1-norm-bounded uncertainties. We show that the solution to this problem demands the computation of the minimum of a piece-wise realrational function ( ), called the stability radius function. It is then shown that the calculations of ( ) at the intersection points where ( ) changes its representation and at the stationary points where ( ) = 0 can be reduced to two sets of eigenvalue problems of matrices of the form H -1 ÿ H , where both H ÿ and H are frequency-independent Hurwitz matrices. Using root locus technique, we analyze this function further and prove that, in some special cases, the minimum of this function can be achieved only at the intersection points. Extensions of the eigenvalue approach to cover other robust stability problems are also discussed.