Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Babiarz, Artur; Banshchikova, I.N.; Czornik, Adam; Makarov, E. K.; Niezabitowski, Michał; Popova, S. N.

doi:10.1007/978-3-030-35502-9_5

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…Stabilization problems for nonlinear time-invariant discrete-time systems were studied in [1][2][3][4][5][6][7][8][9]. Pole placement problems for time-varying discrete-time systems were studied in [10] for periodic systems, and in [11][12][13][14] for arbitrary non-periodic time-varying systems.…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Czornik,

Makarov,

Niezabitowski

et al. 2021

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Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.

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Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Czornik,

Makarov,

Niezabitowski

et al. 2021

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“…In a series of studies [13][14][15][16][17], the results on arbitrary assignability of Lyapunov exponents and other Lyapunov invariants for system (2) in finite-dimensional spaces were proved, based on the property of uniform complete controllability in the sense of Kalman. 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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Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Cited by 2 publications

References 8 publications

Archives of Control Sciences

Archives of Control Sciences

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

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