Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities

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Previous article Next article Stability Conditions for Systems with Monotone and Slope-Restricted NonlinearitiesG. Zames and P. L. FalbG. Zames and P. L. Falbhttps://doi.org/10.1137/0306007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. I. Lur'e, Some Nonlinear Problems in the Theory of Automatic Control, Her Majesty's Stationery office, London, 1957 Google Scholar[2] V.-M. Popov, Absolute stability of nonlinear systems of automatic control, Automat. Remote Control, 22 (1961), 857–875 MR0133563 0107.29601 Google Scholar[3A] G. Zames, On the stability of nonlinear, time-varying feedback systems, Proc. National Electronics Conference, Vol. 20, 1964, 725–730 Google Scholar[3B] G. Zames, On the input-output stability of time-varying nonlinear feedback systems, Parts I, II, IEEE Trans. Automatic Control, AC-11 (1966), 228--238, 465--476 10.1109/TAC.1966.1098316 CrossrefISIGoogle Scholar[4] R. W. Brockett and , J. W. Willems, Frequency domain stability criteria, Parts I, II, Proc. Joint Automatic Control Conference, Troy, New York, 1965, 735–747 Google Scholar[5] V. A. Yakubovich, Frequency conditions for the absolute stability and dissipativity of control systems with a single differentiable nonlinearity, Soviet Math. Dokl., 6 (1965a), 98–101 0142.36301 Google Scholar[6] Kumpati S. Narendra and , Charles P. Neuman, Stability of a class of differential equations with a single monotone nonlinearity, SIAM J. Control, 4 (1966), 295–308 10.1137/0304025 MR0204176 0196.46002 LinkGoogle Scholar[7] B. D. O. Anderson, Stability of control systems with multiple nonlinearities, J. Franklin Inst., 282 (1966), 155–160 10.1016/0016-0032(66)90317-6 MR0204173 0201.47404 CrossrefISIGoogle Scholar[8] A. G. Dewey and , E. I. Jury, A stability inequality for a class of nonlinear feedback systems, IEEE Trans. Automatic Control, AC-11 (1966), 54–62 10.1109/TAC.1966.1098236 MR0191679 CrossrefISIGoogle Scholar[9] C. T. Lee and , C. A. Desoer, Stability of single-loop nonlinear feedback systems, Rep., ERL 66-13, Electronics Research Laboratory, University of California, Berkeley, 1966 Google Scholar[L0A] R. P. O'Shea, A combined frequency-time domain stability criterion for autonomous continuous systems, Proc. Joint Automatic Control Conference, Seattle, Washington, 1966, 832–840 Google Scholar[10B] R. P. O'Shea, An improved frequency-time domain stability criterion for continuous autonomous systems, unpublished report. Google Scholar[11] G. Zames and , P. L. Falb, On the stability of systems with monotone and odd monotone nonlinearities, IEEE Trans. Automatic Control, AC-12 (1967), 221–223 10.1109/TAC.1967.1098520 CrossrefISIGoogle Scholar[12] N. Dunford and , J. T. Schwartz, Linear Operators, I, Interscience, New York, 1966 Google Scholar[13] R. E. A. C. Paley and , N. Wiener, Fourier Transforms in the Complex Domain, American Mathematical Society, Providence, Rhode Island, 1934 0011.01601 Google Scholar[14] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, Oxford, 1964 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The Energy Technique for the Six-Step BDF MethodGeorgios Akrivis, Minghua Chen, Fan Yu, and Zhi ZhouSIAM Journal on Numerical Analysis, Vol. 59, No. 5 | 23 September 2021AbstractPDF (629 KB)Analysis and Design of Optimization Algorithms via Integral Quadratic ConstraintsSIAM Journal on Optimization, Vol. 26, No. 1 | 7 January 2016AbstractPDF (647 KB)Delay-Integral-Quadratic Constraints and Absolute Stability of Time-Periodic Feedback SystemsSIAM Journal on Control and Optimization, Vol. 47, No. 6 | 7 January 2009AbstractPDF (236 KB)Global Variation Criteria for the $L_2 $-Stability of Nonlinear Time Varying SystemsSIAM Journal on Mathematical Analysis, Vol. 9, No. 3 | 17 February 2012AbstractPDF (1206 KB)Hilbert Networks. 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