On the Lyapunov Stability Criteria

Abstract

Previous article Next article On the Lyapunov Stability CriteriaJohn Jones, Jr.John Jones, Jr.https://doi.org/10.1137/0113061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[2] David H. Carlson and , Hans Schneider, Inertia theorems for matrices: the semidefinite case, J. Math. Anal. Appl., 6 (1963), 430–446 10.1016/0022-247X(63)90023-4 MR0148678 0192.13402 CrossrefGoogle Scholar[3] Wolfgang Hahn, Eine Bemerkung zur zweiten Methode von Ljapunov, Math. Nachr., 14 (1955), 349–354 (1956) MR0082013 0071.30701 CrossrefGoogle Scholar[4] John Jones, Jr., A Diophantine matrix equation, Amer. Math. Monthly, 62 (1955), 244–247 MR0068511 0065.24804 CrossrefGoogle Scholar[5A] R. E. Kalman and , J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. I. Continuous-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), 371–393 MR0157810 CrossrefGoogle Scholar[5B] R. E. Kalman and , J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. II. Discrete-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), 394–400 MR0157811 CrossrefGoogle Scholar[6] Joseph LaSalle and , Solomon Lefschetz, Stability by Liapunov's direct method, with applications, Mathematics in Science and Engineering, Vol. 4, Academic Press, New York, 1961vi+134 MR0132876 0098.06102 Google Scholar[7] Solomon Lefschetz, Some mathematical considerations on nonlinear automatic controls, Contributions to Differential Equations, 1 (1963), 1–28 MR0155068 0126.30502 Google Scholar[8] A. M. Lyapunov, Problem général de la stabilité du mouvementAnnals of Matheimatics Study No. 17, Princeton University Press, Princeton, 1947 Google Scholar[9] Alexander Ostrowski and , Hans Schneider, Some theorems on the inertia of general matrices, J. Math. Anal. Appl., 4 (1962), 72–84 10.1016/0022-247X(62)90030-6 MR0142555 0112.01401 CrossrefGoogle Scholar[10] P. C. Parks, A new proof of the Routh-Hurwitz stability criterion using the second method of Liapunov, Proc. Cambridge Philos. Soc., 58 (1962), 694–702 MR0144032 0111.28303 CrossrefISIGoogle Scholar[11] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[12] William E. Roth, The equations $AX-YB=C$ and $AX-XB=C$ in matrices, Proc. Amer. Math. Soc., 3 (1952), 392–396 MR0047598 0047.01901 ISIGoogle Scholar[13] Olga Taussky, A remark on a theorem of Lyapunov, J. Math. Anal. Appl., 2 (1961), 105–107 10.1016/0022-247X(61)90048-8 MR0124335 0158.28203 CrossrefGoogle Scholar[14] O. Taussky and , H. Wielandt, On the matrix function $AX+X\sp{\prime} A\sp{\prime}$, Arch. Rational Mech. Anal., 9 (1962), 93–96 10.1007/BF00253335 MR0132751 0101.25402 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 13, Issue 4| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:14 August 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113061Article page range:pp. 941-945ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics