On the stability of Lyapunov exponents of discrete linear systems

Czornik, Adam; Nawrat, Aleksander; Niezabitowski, Michał

doi:10.23919/ecc.2013.6669149

Cited by 41 publications

(32 citation statements)

References 8 publications

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“…This concept may be defined in several ways and even in the finite-dimensional case these different concepts are not equivalent. The joint spectral radius and subradius are closely connected to Lyapunov exponents of (3), see [13,[15][16][17][18][19], and Bohl exponents, see [1,11,14,21,43,44]. The following theorem contains the relation between the joint spectral radius and absolute stability of DLI (Σ).…”

Section: Definition 1 DLI (σ) Is Called Absolute Stable If and Only Imentioning

confidence: 99%

Estimation of the Joint Spectral Radius

Czornik

Jurgaś

Niezabitowski

2015

Advances in Intelligent Systems and Computing

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The joint spectral radius of a set of matrices is a generalization of the concept of spectral radius of a matrix. Such notation has many applications in the computer science, and more generally in applied mathematics. It has been used, for example in graph theory, control theory, capacity of codes, continuity of wavelets, overlap-free words, trackable graphs. It is impossible to provide analytic formulae for this quantity and therefore any estimation are highly desired. The main result of this paper is to provide an estimation of the joint spectral radius in the terms of matrices norms and spectral radii.

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Section: Definition 1 DLI (σ) Is Called Absolute Stable If and Only Imentioning

confidence: 99%

Estimation of the Joint Spectral Radius

Czornik

Jurgaś

Niezabitowski

2015

Advances in Intelligent Systems and Computing

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“…. , s. The next theorem [10] constitutes discrete-time version of Malkin's (see [13]) sufficient condition for continuity of Lyapunov exponents.…”

Section: Definition 2 the Lyapunov Exponents Of System (1) Are Calledmentioning

confidence: 99%

On a continuity of characteristic exponents of linear discrete time-varying systems

Czornik¹,

Mokry²,

Niezabitowski³

2012

Archives of Control Sciences

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“…The Lyapunov, Bohl and Perron exponents and stability of time-varying discrete-time linear systems have been investigated in [3][4][5][6][7][8]. The positivity and stability of fractional time varying discrete-time linear systems have been addressed in [9][10][11][12][13] and the stability of continuous-time linear systems with delays in [14].…”

Section: Introductionmentioning

confidence: 99%