2010/01/19 by Aleksandar Gjurchinovski, Viktor Urumov · 39 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Computer science #Control (management) #Control engineering #Control system #Control theory (sociology) #Control variable #Engineering #Feedback control #Frequency domain #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Scalar (mathematics) #Stability (learning theory) #Time domain #Variable (mathematics) #math-ph #math.MP #nlin.CD #physics.gen-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.81.016209
published in Physical Review E 81(1), 016209 (American Physical Society) · 13 pages, 8 figures, RevTeX, accepted for publication in Physical Review E
openalex publication_date 2010/01/19 · arxiv created 2010/07/06 · arxiv updated 2010/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already infinite-dimensional before the delayed feedback control is turned on. When the frequency of the modulation is large compared to the system's dynamics, the analytic approach consists of relating the stability properties of the resulting variable-delay system with those of an analogous distributed-delay system. Otherwise, the stability domains are obtained by a numerical integration of the linearized variable-delay system. The analysis shows that the control domains are significantly larger than those in the usual time-delayed feedback control, and that the complexity of the domain structure depends on the form and the frequency of the delay modulation.