Title

Fejér Polynomials and Chaos

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

xn+1=f(xn) (1)

can be robustly stabilized by a nonlinear control

u=−∑j=1N−1εj(f(xn−j+1)−f(xn−j)), |εj| < 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.

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