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Oscillations of Interconnected Systems with C0 Nonlinearities

Published online by Cambridge University Press:  17 February 2009

Xiangjian He
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Abstract

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In this paper we establish conditions which ensure the existence of self-excited oscillations in complex dynamical systems with nondifferentiable nonlinearities, by considering those types of systems which can be viewed as an interconnection of several simpler subsystems. We find that the nonlinear terms of the system in which we are interested do not need to satisfy the Lipschitz condition.

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 1 , July 1996 , pp. 41 - 62
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Bergen, A. R., Chua, L. O., Mees, A. I. and Szeto, E. W., “Error bounds for general describing function problems”, IEEE Trans. Circuit Syst. CAS-29 (1982) 345–354.Google Scholar
[2]Callier, F. M., Chan, W. S. and Desoer, C. A., “Input-output stability theory of interconnected systems using decomposition: an improved formulation”, IEEE Trans. Automat. Contr. AC-23 (1978) 150–163.CrossRefGoogle Scholar
[3]Chen, S., “Disconjugacy, disfocality, and oscillation of second order difference equations”, J. of Differential Eqns 107 (1994) 383–394.CrossRefGoogle Scholar
[4]Dunford, N. and Schwartz, J. T., Linear operators (Interscience Publishers, New York, 1966).Google Scholar
[5]Fiedler, M. and Ptak, V., “On matrices with non-positive off-diagonal elements and positive principal minors”, Czeck. Math. J. 12 (1962) 382–400.CrossRefGoogle Scholar
[6]Michel, A. N. and Miller, R. K., Qualitative analysis of large scale dynamical systems (Academic Press, New York, 1977).Google Scholar
[7]Michel, A. N., Miller, R. K. and Tang, W., “Lyaponov stability of interconnected systems: decomposition into strongly connected subsystems”, IEEE Trans. Circuits Syst. CAS-25 (1978) 799–809.Google Scholar
[8]Miller, R. K. and Michel, A. N., “On the response of nonlinear multivariable interconnected feedback systems to periodic input signals”, IEEE Trans. Circuits Syst. CAS-27 (1980) 1088–1097.CrossRefGoogle Scholar
[9]Miller, R. K. and Skar, S. J., “On existence of limit cycles in systems with discontinuous nonlinear terms”, Rocky Mountain J. of Math 12 (1982) 707–721.CrossRefGoogle Scholar
[10]Skar, S. J., Miller, R. K. and Michel, A. N., “On non-existence of limit cycles in interconnected systems”, IEEE Trans. Automatic Control AC-26 (1981) 669–676.CrossRefGoogle Scholar
[11]Skar, S. J., Miller, R. K. and Michel, A. N., “On existence and nonexistence of limit cycles in interconnected systems”, IEEE Trans. Automatic Control AC-26 (1981) 1153–1168.Google Scholar