On the spectral set of a linear discrete system with stable Lyapunov exponents

Banshchikova, I.N.; Popova, S. N.

doi:10.20537/vm160102

Cited by 10 publications

(16 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The perturbation R(•) = R(t) t∈Z ⊂ M n (K) will be called a multiplicative perturbation of system (2). Definition 7 (see [44]): A multiplicative perturbation R(•) is called admissible if the sequence R(t) t∈Z is a Lyapunov sequence.…”

Section: Local Lyapunov Reducibilitymentioning

confidence: 99%

“…Let us notice that all time-invariant or all periodic systems are regular. Definition 14 (see [44]): The Lyapunov spectrum of system ( 2) is called stable if for any ε > 0 there exists…”

Section: Local Assignability Of the Lyapunov Spectrummentioning

confidence: 99%

“…Later the stability property of the Lyapunov spectrum for these systems was investigated in [48], [49]. The study of this property for discrete-time systems was started in [44].…”

Section: Local Assignability Of the Lyapunov Spectrummentioning

confidence: 99%

See 2 more Smart Citations

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

et al. 2021

View full text Add to dashboard Cite

We consider a linear discrete time-varying input-output system. Our goal is to study the problem of local assignability of the Lyapunov spectrum by static output feedback control. To this end we introduce the notion of uniform consistency for discrete-time linear systems which is the extension of the notion of uniform complete controllability to input-output systems. The property of uniform consistency is investigated, some necessary and sufficient conditions for this property are obtained. The notion of uniform local attainability is introduced for the closed-loop system. We prove that uniform consistency implies uniform local attainability of the closed-loop system. The property of local Lyapunov reducibility is introduced for the closed-loop system. We prove that uniform local attainability implies local Lyapunov reducibility. We prove that, for a locally Lyapunov reducible system, the Lyapunov spectrum is locally assignable, if the free system is diagonalizable or regular (in the Lyapunov sence) or has the stable Lyapunov spectrum.INDEX TERMS linear discrete time-varying input-output systems, local assignability, Lyapunov spectrum, pole assignment problem, static output feedback, uniform consistency.

show abstract

Section: Local Lyapunov Reducibilitymentioning

confidence: 99%

“…Let us notice that all time-invariant or all periodic systems are regular. Definition 14 (see [44]): The Lyapunov spectrum of system ( 2) is called stable if for any ε > 0 there exists…”

Section: Local Assignability Of the Lyapunov Spectrummentioning

confidence: 99%

See 1 more Smart Citation

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

et al. 2021

View full text Add to dashboard Cite

show abstract

“…They showed that in order for the stability of the Lyapunov spectrum of system (2) to hold, it is necessary and sufficient that this system can be reduced to a block-triangular form by some Lyapunov transformation, such that the blocks are integrally separated [9] and for each block, the upper and lower central exponents [7,8,22] coincide. Similar conditions hold for linear discrete-time systems [3]. It is important to notice that, in general these conditions are unverifiable, since for their application we must transform system (2) (or system (4)) into some special form by Lyapunov transformation, but the algorithms to construct this transformation are unknown.…”

Section: Introductionmentioning

confidence: 95%

“…This property can be called the openness of the Lyapunov spectrum of system (2) (or system (4)). Some results on the openness for continuous-time systems were obtained in [20] and for discrete-time systems in [3].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov spectra behavior for linear discrete-time systems under small perturbations

Czornik,

Makarov,

Niezabitowski

et al. 2021

Preprint

View full text Add to dashboard Cite

We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.

show abstract

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Babiarz

Banshchikova

Czornik

et al. 2020

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

On the spectral set of a linear discrete system with stable Lyapunov exponents

Abstract: All Russian mathematical portal I. N. Banshchikova, S. N. Popova, On the spectral set of a linear discrete system with stable Lyapunov exponents, Vestn.

Cited by 10 publications

References 0 publications

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

Lyapunov Spectrum Local Assignability of Linear Discrete Time-Varying Systems by Static Output Feedback

Lyapunov spectra behavior for linear discrete-time systems under small perturbations

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Contact Info

Product

Resources

About