A generalized Kharitonov theorem for quasi-polynomials and entire functions occurring in systems with multiple and distributed delays

Vadim Olshevsky; M. Lev Sakhnovich

doi:10.1117/12.621565

16 September 2005 A generalized Kharitonov theorem for quasi-polynomials and entire functions occurring in systems with multiple and distributed delays

Vadim Olshevsky, M. Lev Sakhnovich

Author Affiliations +

Proceedings Volume 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV; 591011 (2005) https://doi.org/10.1117/12.621565
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

The classical Kharitonov theorem on interval stability cannot be carried over from polynomials to arbitrary entire functions. In this paper we identify a class of entire functions for which the desired generalization of the Kharitonov theorem can be proven. The class is wide enough to include classes quasi-polynomials occurring in the study of retarded systems with time delays, and some classes of entire functions that could be useful in studying systems with distributed delays. We also derive results for matrix polynomials and matrix entire functions.

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Vadim Olshevsky and M. Lev Sakhnovich "A generalized Kharitonov theorem for quasi-polynomials and entire functions occurring in systems with multiple and distributed delays", Proc. SPIE 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV, 591011 (16 September 2005); https://doi.org/10.1117/12.621565

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