Pyragas stabilizability via delayed feedback with periodic control gain

Abstract In this paper for the unstable periodic solution of nonlinear differential equation, Pyragas stabilizability problem is studied. An algorithm of stabilization via periodical delayed feedback is obtained. The consideration is based on the theory of nonstationary stabilization.

[1]  G. Leonov Linear non-stationary stabilization algorithms and Brockett's problem , 2001 .

[2]  Guang-Ren Duan,et al.  Stabilization of some linear systems with both state and input delays , 2012, Syst. Control. Lett..

[3]  L. Bécu,et al.  Evidence for three-dimensional unstable flows in shear-banding wormlike micelles. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  H. G. Schuster,et al.  CONTROL OF CHAOS BY OSCILLATING FEEDBACK , 1997 .

[5]  Gennady A. Leonov BROCKETT'S PROBLEM IN THE THEORY OF STABILITY OF LINEAR DIFFERENTIAL EQUATIONS , 2002 .

[6]  R. Jayanth,et al.  たんぱく質の幾何:水素結合,立体構造および周辺コンパクトチューブ , 2006 .

[7]  Andreas Amann,et al.  Analytical limitation for time-delayed feedback control in autonomous systems. , 2011, Physical review letters.

[8]  M. M. Shumafov,et al.  Stabilization of Controllable Linear Systems , 2010 .

[9]  H. Nakajima On analytical properties of delayed feedback control of chaos , 1997 .

[10]  Hans Crauel,et al.  Stabilization of Linear Systems by Noise , 1983 .

[11]  M. Ikeda,et al.  Stabilization of Linear Systems , 1972 .

[12]  Tamás Insperger,et al.  Act-and-wait concept for continuous-time control systems with feedback delay , 2006, IEEE Transactions on Control Systems Technology.

[13]  Kestutis Pyragas,et al.  Stabilization of an unstable steady state in a Mackey-Glass system , 1995 .

[14]  R. Brockett A stabilization problem , 1999 .

[15]  Kestutis Pyragas,et al.  Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: theory and experiment. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

[17]  G. Leonov,et al.  Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications , 1996 .

[18]  Kestutis Pyragas Control of chaos via extended delay feedback , 1995 .

[19]  Li︠u︡dmila I︠A︡kovlevna Adrianova Introduction to linear systems of differential equations , 1995 .

[20]  J. Hale Theory of Functional Differential Equations , 1977 .

[21]  V Flunkert,et al.  Beyond the odd number limitation: a bifurcation analysis of time-delayed feedback control. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  H. Nakajima,et al.  Limitation of generalized delayed feedback control , 1998 .

[23]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[24]  K Pyragas,et al.  Delayed feedback control of the Lorenz system: an analytical treatment at a subcritical Hopf bifurcation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.