A matrix equation related to a non-oscillation criterion and Liapunov stability
Author:
William T. Reid
Journal:
Quart. Appl. Math. 23 (1965), 83-87
MSC:
Primary 15.35
DOI:
https://doi.org/10.1090/qam/176997
MathSciNet review:
176997
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Additional Information
- Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0122820
- Wolfgang Hahn, Theorie und Anwendung der direkten Methode von Ljapunov, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 22, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959 (German). MR 0106314
- R. E. Kalman, Y. C. Ho, and K. S. Narendra, Controllability of linear dynamical systems, Contributions to Differential Equations 1 (1963), 189–213. MR 155070
- Joseph LaSalle and Solomon Lefschetz, Stability by Liapunov’s direct method, with applications, Mathematics in Science and Engineering, Vol. 4, Academic Press, New York-London, 1961. MR 0132876
- J. P. LaSalle, The time optimal control problem, Contributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, pp. 1–24. MR 0145169
- William T. Reid, Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems, Pacific J. Math. 13 (1963), 665–685. MR 155049
- William T. Reid, Principal solutions of nonoscillatory linear differential systems, J. Math. Anal. Appl. 9 (1964), 397–423. MR 168854, DOI https://doi.org/10.1016/0022-247X%2864%2990026-5
R. Bellman, Introduction to matrix analysis, McGraw-Hill, 1960
W. Hahn, Theorie und Anwendung der direkten Methode von Ljapunov, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 22, Springer-Verlag, 1959
R. E. Kalman, Y. C. Ho and K. S. Narendra, Controllability of linear dynamical systems, Contributions to Differential Equations, Vol. 1, Interscience, 1963, pp. 189–213
J. LaSalle and S. Lefschetz, Stability by Liapunov’s direct method with applications, Academic Press, 1961
J. P. LaSalle, The time optimal control problem, Contributions to the Theory of non-linear Oscillations, vol. 5, Princeton University Press, 1960, pp. 1–24
W. T. Reid, Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems, Pacific J. Math. 13 (1963) 665-685
W. T. Reid, Principal solutions of non-oscillatory linear differential systems, to appear in J. Math. Anal, and Appl.
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Article copyright:
© Copyright 1965
American Mathematical Society