Stabilization of oscillations from a monoparametric family of the autonomous system

Barabanov, I. N.; Тхай, В. Н.

doi:10.1134/s0005117909020027

Cited by 4 publications

(3 citation statements)

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“…The ordinary point for the second-order system was studied previously in [5], consideration was also given to the stabilization of the oscillations of the generating system by small periodic controls [14]. The present paper generalizes these results to the case of the multidimensional system.…”

Section: Introductionmentioning

confidence: 58%

“…The problem of stabilizing oscillations of the family Σ where the period depends on one parameter was solved in [14]. A deviation-linear and time-periodic smooth control is used.…”

Section: Problem Of Oscillation Stabilizationmentioning

confidence: 99%

“…We assume that system (B) is asymptotically stable. Then, the solution of the problem of stabilization of system (A) is borrowed from [14].…”

Section: Problem Of Oscillation Stabilizationmentioning

confidence: 99%

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Quasiautonomous system: Oscillations, stability, and stabilization at the ordinary point of the family of periodic solutions

Barabanov

Тхай

2013

Autom Remote Control

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Consideration was given to the single-frequency oscillations of the periodic system allied to the nonlinear multidimensional autonomous system. It was assumed that the generating autonomous system admits a family of solutions with period depending on a single parameter: all points of the family break down into the ordinary points whose derivative of the period with respect to the parameter is other than zero and the critical points where this derivative vanishes. Generation of oscillations and their stability at the ordinary point of the family were studied. These problems were solved earlier for the second-order system.

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Section: Introductionmentioning

confidence: 58%

“…The problem of stabilizing oscillations of the family Σ where the period depends on one parameter was solved in [14]. A deviation-linear and time-periodic smooth control is used.…”

Section: Problem Of Oscillation Stabilizationmentioning

confidence: 99%