On robust Hurwitz polynomials
- 1 October 1987
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 32 (10) , 909-913
- https://doi.org/10.1109/tac.1987.1104459
Abstract
In this note, Kharitonov's theorem on robust Hurwitz polynomials is simplified for low-order polynomials. Specifically, for n = 3, 4 , and 5, the number of polynomials required to check robust stability is one, two, and three, respectively, instead of four. Furthermore, it is shown that for n \geq 6 , the number of polynomials for robust stability checking is necessarily four, thus further simplification is not possible. The same simplifications arise in robust Schur polynomials by using the bilinear transformation. Applications of these simplifications to two-dimensional polynomials as well as to robustness for single parameters are indicated.Keywords
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