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Silviu-iulian Niculescu - One of the best experts on this subject based on the ideXlab platform.
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Characterizing the Codimension of Zero Singularities for Time-Delay Systems
Acta Applicandae Mathematicae, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:The analysis of time-delay systems mainly relies on detecting and understanding the spectral values bifurcations when crossing the imaginary axis. This paper deals with the zero singularity, essentially when the zero spectral value is multiple. The simplest case in such a configuration is characterized by an Algebraic Multiplicity two and a geometric Multiplicity one, known as the Bogdanov-Takens singularity. Moreover, in some cases the codimension of the zero spectral value exceeds the number of the coupled scalar-differential equations. Nevertheless, to the best of the author’s knowledge, the bounds of such a Multiplicity have not been deeply investigated in the literature. It is worth mentioning that the knowledge of such an information is crucial for nonlinear analysis purposes since the dimension of the projected state on the center manifold is none other than the sum of the dimensions of the generalized eigenspaces associated with spectral values with zero real parts. Motivated by a control-oriented problems, this paper provides an answer to this question for time-delay systems, taking into account the parameters’ Algebraic constraints that may occur in applications. We emphasize the link between such a problem and the incidence matrices associated with the Birkhoff interpolation problem. In this context, symbolic algorithms for LU-factorization for functional confluent Vandermonde as well as some classes of bivariate functional Birkhoff matrices are also proposed.
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tracking the Algebraic Multiplicity of crossing imaginary roots for generic quasipolynomials a vandermonde based approach
IEEE Transactions on Automatic Control, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the author's knowledge, the Multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the Multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a Multiplicity is provided. Namely, it is shown that the zero spectral value Multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the Multiplicity of crossing imaginary roots $j\omega$ where $\omega\neq 0$ and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szego generic bound arising from the principle argument is established.
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Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach
IEEE Transactions on Automatic Control, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the author's knowledge, the Multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the Multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a Multiplicity is provided. Namely, it is shown that the zero spectral value Multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the Multiplicity of crossing imaginary roots jω where ω ≠ 0 and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szegö generic bound arising from the principle argument is established.
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Computing the codimension of the singularity at the origin for delay systems in the regular case: A vandermonde-based approach
2014 European Control Conference (ECC), 2014Co-Authors: Islam Boussaada, Dina-alina Irofti, Silviu-iulian NiculescuAbstract:The analysis of time-delay systems mainly relies on the identification and the understanding of the spectral values bifurcations when crossing the imaginary axis. One of the most important type of such singularities is when the zero spectral value is multiple. The simplest case in such a configuration is characterized by an Algebraic Multiplicity two and a geometric Multiplicity one known as Bogdanov-Takens singularity. Moreover, in some circumstances the codimension of the zero spectral value exceeds the dimension of the delay-free system of differential equations. To the best of the authors' knowledge, the bound of such a Multiplicity was not deeply investigated in the literature. This paper provides an answer to this question for time-delay systems with linear part characterized in the Laplace domain by a quasipolynomial function with non sparse polynomials and without coupling delays.
Islam Boussaada - One of the best experts on this subject based on the ideXlab platform.
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Characterizing the Codimension of Zero Singularities for Time-Delay Systems
Acta Applicandae Mathematicae, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:The analysis of time-delay systems mainly relies on detecting and understanding the spectral values bifurcations when crossing the imaginary axis. This paper deals with the zero singularity, essentially when the zero spectral value is multiple. The simplest case in such a configuration is characterized by an Algebraic Multiplicity two and a geometric Multiplicity one, known as the Bogdanov-Takens singularity. Moreover, in some cases the codimension of the zero spectral value exceeds the number of the coupled scalar-differential equations. Nevertheless, to the best of the author’s knowledge, the bounds of such a Multiplicity have not been deeply investigated in the literature. It is worth mentioning that the knowledge of such an information is crucial for nonlinear analysis purposes since the dimension of the projected state on the center manifold is none other than the sum of the dimensions of the generalized eigenspaces associated with spectral values with zero real parts. Motivated by a control-oriented problems, this paper provides an answer to this question for time-delay systems, taking into account the parameters’ Algebraic constraints that may occur in applications. We emphasize the link between such a problem and the incidence matrices associated with the Birkhoff interpolation problem. In this context, symbolic algorithms for LU-factorization for functional confluent Vandermonde as well as some classes of bivariate functional Birkhoff matrices are also proposed.
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tracking the Algebraic Multiplicity of crossing imaginary roots for generic quasipolynomials a vandermonde based approach
IEEE Transactions on Automatic Control, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the author's knowledge, the Multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the Multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a Multiplicity is provided. Namely, it is shown that the zero spectral value Multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the Multiplicity of crossing imaginary roots $j\omega$ where $\omega\neq 0$ and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szego generic bound arising from the principle argument is established.
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Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach
IEEE Transactions on Automatic Control, 2016Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the author's knowledge, the Multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the Multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a Multiplicity is provided. Namely, it is shown that the zero spectral value Multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the Multiplicity of crossing imaginary roots jω where ω ≠ 0 and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szegö generic bound arising from the principle argument is established.
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Computing the codimension of the singularity at the origin for delay systems in the regular case: A vandermonde-based approach
2014 European Control Conference (ECC), 2014Co-Authors: Islam Boussaada, Dina-alina Irofti, Silviu-iulian NiculescuAbstract:The analysis of time-delay systems mainly relies on the identification and the understanding of the spectral values bifurcations when crossing the imaginary axis. One of the most important type of such singularities is when the zero spectral value is multiple. The simplest case in such a configuration is characterized by an Algebraic Multiplicity two and a geometric Multiplicity one known as Bogdanov-Takens singularity. Moreover, in some circumstances the codimension of the zero spectral value exceeds the dimension of the delay-free system of differential equations. To the best of the authors' knowledge, the bound of such a Multiplicity was not deeply investigated in the literature. This paper provides an answer to this question for time-delay systems with linear part characterized in the Laplace domain by a quasipolynomial function with non sparse polynomials and without coupling delays.
Wang Sheng-hua - One of the best experts on this subject based on the ideXlab platform.
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Spectral Analyse of theTransport Operator with a PeriodicBoundary Conditions in Slab Geometry
Journal of Shangrao Normal College, 2020Co-Authors: Wang Sheng-huaAbstract:The objective of this paper is to analyse some spectral properties of transport operator with anisotropic one-energy inhomogeneous slab geometry in periodic boundary condition. On the fundament of ref.~ [3] It is proved the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite Algebraic Multiplicity in trip, and to prove the existence of the dominant eigenvalue.
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Singular Transport Equations with a Reflecting Boundary Conditions in Slab Geometry
Journal of Nanchang University, 2020Co-Authors: Wang Sheng-huaAbstract:The objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous in slab geometry of reflecting boundary conditions.It proves that the transport operator generates a strongly continuous semigroup and the weak compactness properties of the second-order remained term of the Dyson-Phillips expansion for the semigroup in space,and to obtain the spectrum of the transport operator only consist of,at most,finitely many isolated eigenvalues which have a finite Algebraic Multiplicity in trip.
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The Spectral Analyse of Transport Operator with a Perfect Reflecting Boundary Condition in Slab Geometry
Journal of Jiangxi Normal University, 2020Co-Authors: Wang Sheng-huaAbstract:The objective of this paper is to research spectral analyse of transport operator with anisotropic continuous energy homogeneous slab geometry in perfect reflecting boundary condition.It proves the transport operator generates a strongly continuous group and the compactness properties of the second-order remained term of the Dyson-Phillips expansion for the C_0 group,and to obtain the spectrum of the transport operator only consist of finite isolated eigenvalue which have a finite Algebraic Multiplicity in trip Γ,and to prove the existence of the dominant eigenvalue.
Guo-dong Zhang - One of the best experts on this subject based on the ideXlab platform.
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On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping☆
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Guo-dong ZhangAbstract:Abstract The spectral property of an Euler–Bernoulli beam equation with clamped boundary conditions and internal Kelvin–Voigt damping is considered. The essential spectrum of the system operator is rigorously identified to be an interval on the left real axis. Under some assumptions on the coefficients, it is shown that the essential spectrum contains continuous spectrum only, and the point spectrum consists of isolated eigenvalues of finite Algebraic Multiplicity. The asymptotic behavior of eigenvalues is presented.
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Spectral analysis of a wave equation with Kelvin-Voigt damping
Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 2010Co-Authors: Jun-min Wang, Guo-dong ZhangAbstract:A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum consists of isolated eigenvalues of finite Algebraic Multiplicity, and the continuous spectrum that is identical to the essential spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.
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CDC - Frequency analysis of a wave equation with Kelvin-Voigt damping
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009Co-Authors: Jun-min Wang, Guo-dong ZhangAbstract:A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite Algebraic Multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.
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Frequency analysis of a wave equation with Kelvin-Voigt damping
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009Co-Authors: Jun-min Wang, Guo-dong ZhangAbstract:A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite Algebraic Multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.
Wu Hong-xing - One of the best experts on this subject based on the ideXlab platform.
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The Spectral Analysis of Transport Operator with Continuous Energy in Slab Geometry
Journal of Shangrao Normal College, 2020Co-Authors: Wu Hong-xingAbstract:The objective of this paper is to research the spectrum of transport operator with anisotropic,continuous energy and homogeneous in slab geometry.It obtains that the transport operator A has no complex eigenvalues,and the spectrum of the transport operator A consists of finite real isolated eigenvalues which have a finite Algebraic Multiplicity in trip Pas(A).
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The Spectrum of Transport Operator with Anisotropic in Slab Geometry
Journal of Shangrao Normal College, 2020Co-Authors: Wu Hong-xingAbstract:The objective of this paper is to research the spectrum of transport operator A with anisotropic,monoenergy and homogeneous in slab geometry.It obtains that the transport operator A has no complex eigenvalues, and the spectrum of the transport operator A consists of finite real isolated eigenvalues which have a finite Algebraic Multiplicity in trip Pas(A).
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The Spectral Distribution of Transport Equation with General Boundary Condition
Journal of Shangrao Normal University, 2020Co-Authors: Wu Hong-xingAbstract:The objective of this paper is to research the spectrum of transport equation for anisotropic,continuous energy and homogeneous with general boundary condition in slab geometry of L2 space.It obtains that the transport operator A has no complex eigenvalues,and the spectrum of the transport operator A consists of finite real isolated eigenvalues which have a finite Algebraic Multiplicity in trip Pas(A).
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The Spectral Distribution of a Transport Operator with Periodic Boundary Conditions in Slab Geometry
Journal of Shangrao Normal College, 2020Co-Authors: Wu Hong-xingAbstract:The objective of this paper is to discuss the spectrum of transport operator for anisotropic,continuous energy and homogeneous with periodic boundary conditions in slab geometry.It obtains that the transport operator A has no complex eigenvalue,and the spectrum of the transport operator A consists of finite real isolated eigenvalue which have a finite Algebraic Multiplicity in trip Pas(A).