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Inertia theorems for matrices, controllability, and linear vibrations. (English) Zbl 0288.15015

15A18 Eigenvalues, singular values, and eigenvectors
15A24 Matrix equations and identities
93B99 Controllability, observability, and system structure
70J10 Modal analysis in linear vibration theory
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[1] Carlson, D.; Schneider, H., Inertia theorems: the semidefinite case, J. math. anal. appl., 6, 430-446, (1963) · Zbl 0192.13402
[2] Hautus, M.L.J., Controllability and observability conditions for linear autonomous systems, Nederl. akad. wet. proc., A72, 443-448, (1969) · Zbl 0188.46801
[3] Lee, E.B.; Markus, L., Foundations of optimal control theory, (1967), Wiley New York · Zbl 0159.13201
[4] Müller, P.C., Asymptotische stabilität von linearen mechanischen systemen mit positiv semidefiniter Dämpfungsmatrix, Z. angew. math. mech., 51, T197-T198, (1971) · Zbl 0217.54602
[5] Ostrowski, A.; Schneider, H., Some theorems on the inertia of general matrices, J. math. anal. appl., 4, 72-84, (1962) · Zbl 0112.01401
[6] Snyders, J.; Zakai, M., On nonnegative solutions of the equation AD + DA′ =− C, SIAM J. appl. math., 18, 704-714, (1970) · Zbl 0203.33401
[7] Taussky, O., A generalization of a theorem by Lyapunov, J. soc. ind. appl. math., 9, 640-643, (1961) · Zbl 0108.01202
[8] Zajac, E.E., Comments on “stability of damped mechanical systems” and a further extension, J. aiaa, 3, 1749-1750, (1965)
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