The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenva...The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.展开更多
The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theo...The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account the structure of the matrix. The modified disks of Gershgorin give the opportunity through some geometrical figures called Ovals of Cassini, to consider the form of the matrix in order to determine appropriated bounds for roots. Furthermore, we have seen that, the Hessenbeg matrices are indicated to estimate good bounds for roots of polynomials as far as we become improved bounds for high values of polynomial’s coefficients. But the bounds are better for small values. The aim of the work was to take advantages of this, after introducing the Dehmer’s bound, to find an appropriated property of the Hessenberg form. To illustrate our results, illustrative examples are given to compare the obtained bounds to those obtained through classical methods like Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds.展开更多
This paper presents an Multi-Input Multi-Output(MIMO)analysis to investigate the mutual interactions and small-signal stability of bipolar-type dc microgrids.Since bipolar dc microgrid is replete with power-electronic...This paper presents an Multi-Input Multi-Output(MIMO)analysis to investigate the mutual interactions and small-signal stability of bipolar-type dc microgrids.Since bipolar dc microgrid is replete with power-electronic converters,its dynamics can not be understood unless the interactions among control systems of converters are properly investigated.To tackle the challenge,each converter in microgrid is modeled via an MIMO transfer matrix.Then,the MIMO models are combined together based on the interactions among the control systems of source and load converters.From this integrative MIMO model,the mutual interactions between various input-output pairs are quantified using Gershgorin Band theorem.Also,Singular Value Decomposition(SVD)analysis is carried out to estimate the frequency of unstable poles.Test results not only successfully validate the effectiveness of the MIMO method but also show that the control system of voltage balancer has a major impact on the overall stability of bipolar dc microgrid,making it a suitable location for applying damping systems.展开更多
文摘The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.
文摘The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account the structure of the matrix. The modified disks of Gershgorin give the opportunity through some geometrical figures called Ovals of Cassini, to consider the form of the matrix in order to determine appropriated bounds for roots. Furthermore, we have seen that, the Hessenbeg matrices are indicated to estimate good bounds for roots of polynomials as far as we become improved bounds for high values of polynomial’s coefficients. But the bounds are better for small values. The aim of the work was to take advantages of this, after introducing the Dehmer’s bound, to find an appropriated property of the Hessenberg form. To illustrate our results, illustrative examples are given to compare the obtained bounds to those obtained through classical methods like Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds.
基金This work was supported by the U.S.National Science Foundation under Grant Nos.1647209 and 1611095the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant No.765585.
文摘This paper presents an Multi-Input Multi-Output(MIMO)analysis to investigate the mutual interactions and small-signal stability of bipolar-type dc microgrids.Since bipolar dc microgrid is replete with power-electronic converters,its dynamics can not be understood unless the interactions among control systems of converters are properly investigated.To tackle the challenge,each converter in microgrid is modeled via an MIMO transfer matrix.Then,the MIMO models are combined together based on the interactions among the control systems of source and load converters.From this integrative MIMO model,the mutual interactions between various input-output pairs are quantified using Gershgorin Band theorem.Also,Singular Value Decomposition(SVD)analysis is carried out to estimate the frequency of unstable poles.Test results not only successfully validate the effectiveness of the MIMO method but also show that the control system of voltage balancer has a major impact on the overall stability of bipolar dc microgrid,making it a suitable location for applying damping systems.
