Fejér Polynomials and Chaos

Authors

Dmitriy Dmitrishin, Odessa National Polytechnic UniversityFollow
Anna Khamitova, Georgia Southern UniversityFollow
Alexander M. Stokolos, Georgia Southern UniversityFollow

Document Type

Conference Proceeding

Publication Date

10-15-2014

Publication Title

Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón

DOI

10.1007/978-3-319-10545-1_7

ISBN

978-3-319-10544-4

Abstract

We show that given any μ > 1, an equilibrium x of a dynamic system

x_n+1=f(x_n) (1)

can be robustly stabilized by a nonlinear control

u=−∑_j=1^N−1ε_j(f(x_n−j+1)−f(x_n−j)), |ε_j| < 1, j=1,…,N−1, (2)

for f ′ (x) ∈ (−μ, 1). The magnitude of the minimal value N is of order √μ. The optimal explicit strength coefficients are found using extremal nonnegative Fejér polynomials. The case of a cycle as well as numeric examples and applications to mathematical biology are considered.

Recommended Citation

Dmitrishin, Dmitriy, Anna Khamitova, Alexander M. Stokolos. 2014. "Fejér Polynomials and Chaos." Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón, Constantine Georgakis, Alexander M. Stokolos & Wilfredo Urbina (Ed.), 108: 49-75 Cham, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-10545-1_7 isbn: 978-3-319-10544-4
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/316