Abstract
Sufficient conditions for the asymptotic stability of systems of first order linear differential equations with commuting matrix constant coefficients is studied. Stability criterion in terms of blocks is presented. Inertia of a block circulant matrix is obtained.
2010 Mathematics Subject Classification. 15A27, 34D99, 93D20.
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References
Adhikari S (2000) On symmetrizable systems of second kind. J Appl Mech 67:797–802
Barnett S (1983) Polynomials and linear control systems. Marcel Dekker, New York
Barnett S, Storey C (1970) Matrix methods in stability theory. Thomas Nelson, London
Bellman R (1960) Introduction to matrix analysis. McGraw-Hill, New York
Bhaskar A (2001) Taussky’s theorem, symmetrizability and modal analysis revisited. Proc R Soc Lond A457:2455–2480
Costa C (2001) José Vicente Gonçalves: Matemático... porque Professor! Centro de Estudos de História do Atlântico, Funchal. (ISBN:972-8263-33-3)
Datta BN (1974) A constructive method for finding the Schwarz form of a Hessenberg matrix. IEEE Trans Automat Contr 19:616–617
Davis PJ (1979) Circulant matrices. Wiley, New York
Dennis E, Traub JF, Weber RP (1971) On the matrix polynomial, lambda-matrix and block eigenvalue problems. Computer Science Department, Technical Report, Cornell University, Ithaca, New York and Carnegie-Mellon University, Pittsburgh, Pennsylvania. (Disponível em http://cs-tr.cs.cornell.edu)
Gantmacher FR (1974) The theory of matrices, vol II. Chelsea, New York
Holtz O, Tyaglov M (28 February 2010) Structured matrices, continued fractions, and root localization of polynomials, 78 p, arXiv:0912.4703v2 [math.CA]
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University, New York
Lancaster P, Tismenetsky M (1985) The theory of matrices. Academic, London
Lehnigk SH (1966) Stability theorems for linear motions with an introduction to Lyapunov’s direct method. Prentice-Hall, Englewood Cliffs
Martins F, Pereira E (2007) Block matrices and stability theory. Tatra Mt Math Publ 38:147–162
Pereira E (2003) Block eigenvalues and solutions of differential matrix equations. Mathematical Notes (Miskolc) 4:45–51
Pereira E, Vitória J (2001) Deflation for block eigenvalues of block partitioned matrices with an application to matrix polynomials of commuting matrices. Comput Math Appl 42:1177–1188
Vitória J (1982) Block eigenvalues of block compound matrices. Linear Algebra Appl 47:23–34
Vitória J (1982) A block Cayley Hamilton theorem. Bull Mathemátique (Roumanie) 26:93–97
Vitória J (1988) Some questions of numerical algebra related to differential equations. Numerical Methods (Miskolc, 1986), 127–140, Greenspan D, Rózsa P (eds) Colloquia mathematica cocietatis János Bolyai, vol 50, North-Holland
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Martins, F., Pereira, E., Vicente, M., Vitória, J. (2014). Stability of Matrix Differential Equations with Commuting Matrix Constant Coefficients. In: Fonseca Ferreira, N., Tenreiro Machado, J. (eds) Mathematical Methods in Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7183-3_9
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DOI: https://doi.org/10.1007/978-94-007-7183-3_9
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