On the generalized linear and non-linear DFC in non-linear dynamics

2014/07/24 by Dmitriy Dmitrishin, Dmitrishin, Dmitriy, Anna Khamitova +3
Computer Science · Mathematics · Physics and Astronomy · #93D09 #93D15 #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1407.6488

openalex publication_date 2014/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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