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

MSC:
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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