On the Generalized Linear and Non-Linear DFC in Non-Linear Dynamics

Dmitriy Dmitrishin; Anna Khamitova; Alexander M. Stokolos

On the Generalized Linear and Non-Linear DFC in Non-Linear Dynamics

Dmitriy Dmitrishin, Anna Khamitova, Alexander M. Stokolos

Mathematical Sciences

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Abstract

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the vector-valued setting.

Original language	American English
Journal	arXiv Repository
State	Published - Jul 12 2015

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Education
Mathematics

Keywords

DFC
Dynamics
Linear
Nonlinear

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On the Generalized Linear and Non-Linear DFC in Non-Linear DynamiFinal published version, 2.29 MBLicense: Unspecified

https://arxiv.org/abs/1407.6488

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title = "On the Generalized Linear and Non-Linear DFC in Non-Linear Dynamics",

abstract = " The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the vector-valued setting.",

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AU - Dmitrishin, Dmitriy

AU - Khamitova, Anna

AU - Stokolos, Alexander M.

PY - 2015/7/12

Y1 - 2015/7/12

N2 - The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the vector-valued setting.

AB - The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the vector-valued setting.

KW - DFC

KW - Dynamics

KW - Linear

KW - Nonlinear

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/669

M3 - Article

JO - arXiv Repository

JF - arXiv Repository

ER -

On the Generalized Linear and Non-Linear DFC in Non-Linear Dynamics

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