Vibrational stabilization and calculation formulas for nonlinear time delay systems: Linear multiplicative vibrations

Abstract This paper shows that vibrational control is an effective means of stabilization of nonlinear time lag systems with arbitrarily large but bounded delays. Conditions for stabilizing are formulated and procedures for the synthesis of the corresponding stabilizing vibrations are proposed.

[1]  L. E. El'sgolt's.  Introduction to the Theory of Differential Equations with Deviating Arguments , 1966 .

[2]  Semyon M. Meerkov,et al.  Stability of fast periodic systems , 1985 .

[3]  Semyon M. Meerkov,et al.  Vibrational control of nonlinear systems: Vibrational stabilizability , 1986 .

[4]  Calculation formula for vibrational control of a class of linear time lag systems , 1989 .

[5]  Semyon M. Meerkov,et al.  Vibrational control of nonlinear systems: Vibrational controllability and transient behavior , 1986 .

[6]  J. Bentsman,et al.  Experiment with Vibrational Control of a Laser Illuminated Thermochemical System , 1989, 1989 American Control Conference.

[7]  Joseph Bentsman.  Vibrational control of a class of nonlinear systems by nonlinear multiplicative vibrations , 1987 .

[8]  Erik I. Verriest,et al.  Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior , 1994, IEEE Trans. Autom. Control..

[9]  Erik I. Verriest,et al.  Stability of a continuous stirred reactor with delay in the recycle stream , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  J. Hale,et al.  Stability in Linear Delay Equations. , 1985 .

[11]  Ali Cinar,et al.  Vibrational control of an exothermic reaction in a CSTR: Theory and experiments , 1987 .

[12]  Joseph Bentsman,et al.  Vibrational stabilization of linear time delay systems and its robustness with respect to the delay size , 1989 .

[13]  Semyon Meerkov,et al.  Principle of vibrational control: Theory and applications , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[14]  Jack K. Hale,et al.  Averaging in infinite dimensions , 1990 .

[15]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[16]  Keum Shik Hong,et al.  Vibrational control of nonlinear time lag systems: Vibrational stabilization and transient behavior , 1991, Autom..

[17]  Joseph Bentsman,et al.  Vibrational control of linear time lag systems with arbitrarily large but bounded delays , 1992 .