Abstract
The problem of stability of continuous-time nonlinear systems with non-parametric uncertainty of a linear part and sector uncertainty of its nonlinear part is considered. The proposed robust stability criterion is a natural extension of the circle criterion for absolute stability. The situation with Popov criterion is also discussed; it is demonstrated to be nonrobust for perturbations of a linear part, bounded in H ∞ norm.
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References
A. I. Lurie. On Some Nonlinear Problems in the Theory of Automatic Control. H.M. Stationary Office, London, 1957 (Russian ed. - 1951 ).
M. A. Aizerman and F. R. Gantmacher. Absolute Stability of Regulator Systems. Holden-Day, San Francisco, 1964 (Russian ed. - 1963 ).
S. Lefshetz. Stability of Nonlinear Control Systems. Academic Press, New York, 1963.
V. M. Popov. Hyperstability of Control Systems. Springer, New York, 1973 (Russian ed. - 1971 ).
D. D. Siljak. Nonlinear Systems: the Parameter Analysis and Design. Wiley, New York, 1969.
K. S. Narendra and J. H. Taylor. Frequency Domain Criteria for Absolute Stability. Academic Press, New York, 1973.
M. J. Chen and C. A. Desoer. Necessary and sufficient conditions for robust stability of linear distributed feedback systems. Int. J. Control, 35: 255–267, 1982.
J. C. Doyle and G. Stein. Multivariable feedback design: concepts for a classical/modern synthesis. IEEE Trans. Automatic Control, AC-26: 4–16, 1981.
M. G. Safonov. Stability margins of diagonally perurbed multivariable feedback systems. IEEE Proc., D, 129: 251–256, 1982.
M. Vidyasagar and M. Kimura. Robust controllers of linear multivariable systems. Automatica, 22: 85–94, 1986.
M. Morari and E. Zafirion. Robust Process Control. Prentice Hall, New Jersey, 1989.
V. A. Yakubovitch. Methods of absolute stability theory. In Methods of Research of Nonlinear Automatic Control Systems, ed. Nelesin R. A., Nauka, Moscow, 74–119, (in Russian), 1975.
B. T. Polyak and Ya. Z. Tsypkin. Robust Nyquist criterion. Autom. Remote Control, No. 7, 1992.
Ya. Z. Tsypkin. Stabilization of nonlinear discrete systems under nonparametric uncertainty. Automatica, Kiev, 4: 3–7, 1991 (in Russian).
H. Chapellat, M. Dahleh and S. P. Bhattacharyya. Robust stability under structured and unstructured perturbations. IEEE Trans. Autom. Control, AC-35:11001108, 1990.
B. T. Polyak and Ya. Z. Tsypkin. Robust stability under complex parameter perturbations. Autore. and Remote Control, 52: 1069–1077, 1991.
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© 1992 Birkhäuser Verlag Basel
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Tsypkin, Y.Z., Polyak, B.T. (1992). Robust Absolute Stability of Continuous Systems. In: Mansour, M., Balemi, S., Truöl, W. (eds) Robustness of Dynamic Systems with Parameter Uncertainties. Monte Verità. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7268-3_12
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DOI: https://doi.org/10.1007/978-3-0348-7268-3_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7270-6
Online ISBN: 978-3-0348-7268-3
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