Passivity and linear system stability
Author:
Y. V. Venkatesh
Journal:
Quart. Appl. Math. 34 (1976), 19-27
MSC:
Primary 93D05
DOI:
https://doi.org/10.1090/qam/687250
MathSciNet review:
687250
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Abstract: Using the network concept of passivity (or positive realness), new criteria for stability and instability of linear systems (with time-varying coefficients) are derived.
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- Y. V. Venkatesh, Global variation criteria for stability of linear time-varying systems, SIAM J. Control 9 (1971), 431–440. MR 0299291
R. W. Brockett, Optimisation theory and the converse of the Circle Criterion, Proc. 1965 NEC, pp. 697–701
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E. F. Infante and R. Plaut, Stability of a column subjected to a time dependent axial load, AIAA J. 7, 766–768 (1969)
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E. F. Infante, (a) Stability criteria for nth order homogeneous linear differential equations, in Differential equations and dynamical systems (ed. J. P. LaSalle), Academic Press, New York, 1967, pp. 309–321; (b) On the stability of some linear nonautonomous systems, J. Appl. Mech. 35, 7–12 (1968)
Y. V. Ventakesh, Global variation criteria for the stability of linear time varying systems, SIAM J. Control 9, 431–440 (1971)
R. W. Brockett, Optimisation theory and the converse of the Circle Criterion, Proc. 1965 NEC, pp. 697–701
C. Corduneanu, The application of differential inequalities to the theory of stability, An. Sti. Uni. Al. I. Cuza Iasi Sect. I (N.S.) 6, 47–58 (1960)
T. A. Bickart, Periodically time varying system: an instability criterion, Proc. IEEE 55, no. 12, 2057 (1967)
R. A. Skoog and C. C. G. Lau, Instability of slowly varying systems, IEEE Trans. Automatic Control AC-17, 86–92 (1972)
B. D. O. Anderson, A system theory criterion for positive real matrices, SIAM J. Control 5, 171–182 (1967)
J. R. Dickerson, Stability of systems with parametric excitation, J. Appl. Mech. 37, 228–230 (1970)
E. F. Infante and R. Plaut, Stability of a column subjected to a time dependent axial load, AIAA J. 7, 766–768 (1969)
J. F. Potter, Matrix quadratic solutions, SIAM J. Appl. Math. 14, 496–501 (1966)
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Article copyright:
© Copyright 1976
American Mathematical Society
