On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

Czornik, Adam; Nawrat, Aleksander; Niezabitowski, Michał

doi:10.1080/14689367.2012.748718

Cited by 40 publications

(10 citation statements)

References 25 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: 92%

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: 92%

Estimation of the Joint Spectral Radius

Czornik

Jurgaś

Niezabitowski

2015

Advances in Intelligent Systems and Computing

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“…Since then, they were an object of intensive research and had a number of generalizations and variants [5]- [7]. Also the problem of sensitivity to parameter variation has been widely investigated (see for example [8] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Alternative formulae for lower general exponent of discrete linear time-varying systems

Czornik

Niezabitowski

2015

Journal of the Franklin Institute

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“…In [63] one can find example of calculation of ρ(Σ) for a set of 2-by-2 matrices. Some further results in this direction contains [64].…”

Section: Definitionmentioning

confidence: 99%

Stability and controllability of switched systems

Klamka¹,

Czornik²,

Niezabitowski³

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

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On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

Cited by 40 publications

References 25 publications

Estimation of the Joint Spectral Radius

Estimation of the Joint Spectral Radius

Alternative formulae for lower general exponent of discrete linear time-varying systems

Stability and controllability of switched systems

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