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Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

100%
Zhai G., Xu X., Lin H., Liu D.
International Journal of Applied Mathematics and Computer Science
|
2007
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tom 17
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nr 4
447-454
EN
We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.
2
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On Lie algebras of vector fields related to Riemannian foliations

86%
Rybicki T.
Annales Polonici Mathematici
|
1993
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tom 58
|
nr 2
111-122
EN
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
3
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On roots of the automorphism group of a circular domain in $ℂ^n$

86%
Myszewski J.
Annales Polonici Mathematici
|
1991
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tom 55
|
nr 1
269-276
EN
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in $ℂ^n$ containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
4
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A note on semidirect sum of Lie algebras

72%
Ostrowski T.
Discussiones Mathematicae - General Algebra and Applications
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2013
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tom 33
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nr 2
233-247
EN
In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.
5
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The Leibniz algebras whose subalgebras are ideals

72%
Kurdachenko L. A., Semko N. N., Subbotin I. Y.
Open Mathematics
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2017
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tom 15
|
nr 1
92-100
EN
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
6
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Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical

72%
Camacho L. M., Omirov B. A., Masutova K. K., Rikhsiboev I. M.
Open Mathematics
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2017
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tom 15
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nr 1
1371-1388
EN
All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.
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