The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Augusto Ferrante - One of the best experts on this subject based on the ideXlab platform.
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New Results on the Characterization of Strictly Positive Real Matrix Transfer Functions
IEEE Transactions on Automatic Control, 2021Co-Authors: Mojtaba Hakimi-moghaddam, Augusto FerranteAbstract:In this article, we analyze the high-frequency condition that discriminates strictly positive Real systems from weakly strictly positive Real ones. Different versions of this condition have been proposed in the literature. We consider the general case of multi-input–multi-output (MIMO) systems and derive new equivalent conditions. A graphic interpretation is also presented. In comparison to the existing literature, the conditions derived here are easier to check, especially for large dimension systems and high-order systems. Several illustrative examples are provided to support the results.
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A Direct Proof of the Equivalence of Side Conditions for Strictly Positive Real Matrix Transfer Functions
IEEE Transactions on Automatic Control, 2020Co-Authors: Augusto Ferrante, Alexander Lanzon, Bernard BrogliatoAbstract:This brief note proves in a direct way that two different side conditions, which have been used in the literature to characterize strictly positive Real Matrix transfer functions in the frequency domain, are equivalent.
Rama K. Yedavalli - One of the best experts on this subject based on the ideXlab platform.
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ACC - A New, Necessary and Sufficient condition for Hurwitz Stability of a Real Matrix Without Characteristic Polynomial, Using Qualitative Reasoning
2018 Annual American Control Conference (ACC), 2018Co-Authors: Rama K. YedavalliAbstract:In this paper, we present a new, necessary and sufficient condition for Hurwitz stability of Real Matrix, using qualitative (based solely on sign pattern of the Matrix) reasoning. This new stability condition, completely deviates from the age-old quantitative methods such as the Routh-Hurwitz criterion, Lyapunov Matrix Solution criterion and the related Fuller's criterion, which are all constrained by the similarity transformation phenomenon. Put it another way, this new condition does not need the formation of the characteristic polynomial at all and is based on the direct Matrix entries' information. We propose a new, necessary and sufficient condition for the Hurwitz stability of any Real Matrix, in terms of three ‘critical Matrix indices' each for the original Matrix $A$ and its higher dimensional Bialternate sum Matrix (labeled Fuller's Matrix), denoted by $\mathscr{B}$ . Thus the new necessary and sufficient condition relies on the behavior of a total six ‘critical Matrix indices’. It can be said that through the condition presented in this paper, we are assessing the Hurwitz stability of a Real Matrix without using the Routh-Hurwitz criterion. Examples are given to illustrate the proposed methodology along with a discussion of the attractive ‘convexity’ property of this new condition which is lacking in the current quantitative methods.
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Conditions for Hurwitz Stability/Instability of a Real Matrix via its Sign Pattern with a Necessary and Sufficient Condition for Magnitude Independent Stability
IFAC-PapersOnLine, 2018Co-Authors: Rama K. YedavalliAbstract:Abstract In this paper, we address the issue of discerning the Hurwitz stability/instability of Real Matrix directly from its sign pattern.In that connection, in this paper, we first classify all sign patterns of matrices into three categories, namely i) Qualitative Sign Unstable (QLSU) matrices (i.e. matrices with a sign pattern that it is unstable for any magnitudes in the entries, that is, magnitude independent instability), then ii) Qualitative Sign Stable (QLSS) matrices (i.e. matrices with a sign pattern that it is stable for any magnitudes in the entries, that is, magnitude independent stability) and finally iii) MDSU matrices (which require magnitudes to determine its stability/instability). We then propose a necessary and sufficient condition for a sign Matrix to be QLSS. The proposed necessary and sufficient condition is derived solely based on the nature (signs) of interactions and interconnections (i.e. based only on the signs of the entries of the Matrix), borrowed from ecological principles. The proposed condition in this paper, serves as a better (being much simpler) alternative to the necessary and sufficient condition for QLSS matrices that is available in the ecology literature which uses a complicated test labeled ‘the Color test’. Identifying QLSS/MDSU/QLSU sign structures in a necessary and sufficient way has significant implications in many engineering systems whose dynamics are described by linear state space representation.
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ACC - Analysis of Hurwitz stability/instability of a Real Matrix via the concepts of Qualitative Determinant and Signature of a Matrix
2016 American Control Conference (ACC), 2016Co-Authors: Rama K. YedavalliAbstract:Currently available conditions of Hurwitz stability/instability assessment of a Real Matrix are essentially based on quantitative information (both sign and magnitudes of the entries of the Matrix). Assessing the Hurwitz stability/instability, solely based on sign information, labeled Qualitative (Sign) Stability/Instability is also of much importance as a supplement to these quantitative based results. In this paper, we highlight the importance of the ‘elemental sign structure’ of a Matrix in its Hurwitz stability/instability assessment and present new results in the form of necessary and sufficient conditions. This analysis is done using the concepts of both Quantitative Determinant (involving magnitudes) and the Qualitative Determinant (involving only the sign information of the Matrix elements). Using these metrics, we form the ‘Signature’ of a Real Matrix that reflects the stability/instability nature of the Matrix. The proposed results in this paper are deemed helpful also in solving many other related problems of stability including the testing of robust stability of interval parameter Matrix families, which has attracted intense attention and scrutiny in the last few decades.
Leiba Rodman - One of the best experts on this subject based on the ideXlab platform.
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canonical forms for symmetric skew symmetric Real Matrix pairs under strict equivalence and congruence
Linear Algebra and its Applications, 2005Co-Authors: Peter Lancaster, Leiba RodmanAbstract:A systematic development is made of the simultaneous reduction of pairs of quadratic forms over the Reals, one of which is skew-symmetric and the other is either symmetric or skew-symmetric. These reductions are by strict equivalence and by congruence, over the Reals or over the complex numbers, and essentially complete proofs are presented. The proofs are based on canonical forms attributed to Jordan and Kronecker. Some closely related results which can be derived from the canonical forms of pairs of symmetric/skew-symmetric Real forms are also included. They concern simultaneously neutral subspaces, Hamiltonian and skew-Hamiltonian matrices, and canonical structures of Real matrices which are selfadjoint or skew-adjoint in a regular skew-symmetric indefinite inner product, and Real matrices which are skew-adjoint in a regular symmetric indefinite inner product. The paper is largely expository, and continues the comprehensive account of the reduction of pairs of matrices started in [P. Lancaster, L. Rodman, Canonical forms for hermitian Matrix pairs under strict equivalence and congruence, SIAM Rev., in press].
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Invariant neutral subspaces for symmetric and skew Real Matrix pairs
Canadian Journal of Mathematics, 1994Co-Authors: Peter Lancaster, Leiba RodmanAbstract:AbstractReal Matrix pairs (A,H) satisfying det H ≠ 0, HT = εH, and HA - ηATH, where ε, η take the values +1 or —1, are considered. It is shown that maximal A-invariant H-neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair (A, H). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).
Bernard Brogliato - One of the best experts on this subject based on the ideXlab platform.
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A Direct Proof of the Equivalence of Side Conditions for Strictly Positive Real Matrix Transfer Functions
IEEE Transactions on Automatic Control, 2020Co-Authors: Augusto Ferrante, Alexander Lanzon, Bernard BrogliatoAbstract:This brief note proves in a direct way that two different side conditions, which have been used in the literature to characterize strictly positive Real Matrix transfer functions in the frequency domain, are equivalent.
Jun-e Feng - One of the best experts on this subject based on the ideXlab platform.
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On solutions to the Matrix equations XB−AX=CY and XB−AX^=CY
Journal of the Franklin Institute, 2016Co-Authors: Caiqin Song, Jun-e FengAbstract:Abstract The solution of the generalized Sylvester Real Matrix equation XB − AX = CY is important in stability analysis and controller design in linear systems. This paper presents an explicit solution to the generalized Sylvester Real Matrix equation XB − AX = CY . Based on the derived explicit solution to the considered generalized Sylvester Real Matrix equation, a new approach is provided for obtaining the solutions to the generalized Sylvester quaternion j-conjugate Matrix equation XB − A X ^ = CY using the Real representation of a quaternion Matrix. The closed form solution is established in an explicit form for this generalized Sylvester quaternion j-conjugate Matrix equation. The existing complex representation method requires the coefficient Matrix A to be a block diagonal Matrix over complex field, while it is any suitable dimension quaternion Matrix in the present paper. Therefore, we generalize the existing results.
