Abstract
We show that given any μ > 1, an equilibrium x of a dynamic system (Formula Presented) can be robustly stabilized by a nonlinear control (Formula Presented) for f′(x) ∈ (−μ, 1). The magnitude of the minimal value N is of order (Formula Presented). 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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CITATION STYLE
Dmitrishin, D., Khamitova, A., & Stokolos, A. M. (2014). Fejér polynomials and chaos. In Springer Proceedings in Mathematics and Statistics (Vol. 108, pp. 49–75). Springer New York LLC. https://doi.org/10.1007/978-3-319-10545-1_7
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