Baire classes of Lyapunov invariants

Bykov, V. V.

doi:10.1070/sm8809

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…In recent studies [18][19][20][21][22][23], these results have been partially extended to discrete-time systems. In finite-dimensional spaces, the Lyapunov exponents, the Bohl exponents, and other Lyapunov invariants were studied, for example in [24][25][26] for continuous-time systems and in [27][28][29][30][31][32][33] for discrete-time systems.…”

Section: Introductionmentioning

confidence: 99%

On Assignment of the Upper Bohl Exponent for Linear Time-Invariant Control Systems in a Hilbert Space by State Feedback

Зайцев

Zhuravleva

2020

Mathematics

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We consider a linear continuous-time control system with time-invariant linear bounded operator coefficients in a Hilbert space. The controller in the system has the form of linear state feedback with a time-varying linear bounded gain operator function. We study the problem of arbitrary assignment for the upper Bohl exponent by state feedback control. We prove that if the open-loop system is exactly controllable then one can shift the upper Bohl exponent of the closed-loop system by any pregiven number with respect to the upper Bohl exponent of the free system. This implies arbitrary assignability of the upper Bohl exponent by linear state feedback. Finally, an illustrative example is presented.

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Section: Introductionmentioning

confidence: 99%

On Assignment of the Upper Bohl Exponent for Linear Time-Invariant Control Systems in a Hilbert Space by State Feedback

Зайцев

Zhuravleva

2020

Mathematics

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Baire Classes of Functionals on the Space of Linear Differential Systems

Ravcheev

2019

Diff Equat

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О Существовании Линейной Дифференциальной Системы С Заданными Показателями Перрона

Гаргянц¹,

Gargyants

2019

Известия Российской академии наук. Серия математическая

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Рассматриваются линейные дифференциальные системы с бесконечно дифференцируемыми, но, вообще говоря, неограниченными на полуоси коэффициентами. Доказано, что отображение, сопоставляющее ненулевому решению такой системы значение показателя Перрона на нем, может оказаться произвольной непрерывной функцией, постоянной вдоль всякой проходящей через нуль прямой в пространстве решений. Библиография: 7 наименований.

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Baire classes of Lyapunov invariants

Cited by 3 publications

References 10 publications

On Assignment of the Upper Bohl Exponent for Linear Time-Invariant Control Systems in a Hilbert Space by State Feedback

On Assignment of the Upper Bohl Exponent for Linear Time-Invariant Control Systems in a Hilbert Space by State Feedback

Baire Classes of Functionals on the Space of Linear Differential Systems

О Существовании Линейной Дифференциальной Системы С Заданными Показателями Перрона

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