A short survey on Pyragas time-delay feedback stabilization and odd number limitation. Issue 11 (2015)

• Record Type: Journal Article
• Authors: Kuznetsov, N.V.; Leonov, G.A.; Shumafov, M.M.
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 11(2015)
• Page Start: 706
• Page End: 709
• Publication Date: 2015
• Subjects: delayed feedback control -- stabilization -- equilibrium -- asymptotic stability -- linear controllable system; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.271
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: K. Pyragas (1992) introduced a simple and eficient control scheme, called timedelayed feedback control (TDFC), that stabilizes unstable periodic orbit (UPO) embedded in a chaotic attractor. It turned out that in the case of Pyragas' stationary feedback TDFC works only for a certain class of systems. The odd number limitation (ONL) is that any UPO with an odd number of real Floquet multipliers greater than unity (or with odd number of real-positive Floquet exponents) can never be stabilized by Pyragas' TDFC. In this paper a short survey with recent results on TDFC and ONL is presented.