Abstract
The argument of physical dimension/units is applied to electrical switched circuits, making the topic of the nonlinearity of such circuits simpler. This approach is viewed against the background of a more general outlook (Gluskin in IEEE Circuits Syst. Mag. 56, 58, 60–62, 2009) on singular (switched and sampling) systems. The Appendix suggests some points for the axiomatization of system theory considered as an independent science.
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References
L.O. Chua, A computer-oriented sophomore course on nonlinear circuit analysis. IEEE Trans. Ed. E-12(3), 202–208 (1969)
A.S. Elwakil, Nonautonomous pulse-driven chaotic oscillator based on Chua’s circuit. Microelectron. J. 33, 479–486 (2002)
A.S. Elwakil, M.P. Kennedy, Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices. IEEE Trans. Circuits Syst. I 48, 289–307 (2001)
A.S. Elwakil, S. Ozoguz, Chaos in a pulse-excited resonator with self feedback. Electron. Lett. 39, 831–833 (2003)
E. Gluskin, A point of view on the linearity and nonlinearity of switched systems, in Proceedings of 2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, Eilat, 15–17 Nov. 2006, pp. 110–114
E. Gluskin, The nonlinear-by-switching systems: a heuristic discussion of some singular systems. Manuscript (2007). arXiv:0801.3652v2 [nlin.SI]
E. Gluskin, A small theorem on the nonlinearity of switched systems. AEÜ, Int. J. Electron. Commun. 64(4), 260–265 (2008)
E. Gluskin, On the concept of switching nonlinearity (a comment on ‘Switching control of linear systems for generating chaos’ by X. Liu, K.-L. Teo, H. Zhang and G. Chen). Manuscript (2008). arXiv:0803.3132v2 [nlin.CD]
E. Gluskin, On the mathematical representation of nonlinearity. Manuscript (2008). arXiv:0807.0966v2 [nlin.SI]
E. Gluskin, Switched systems and conceptual basis of circuit theory. IEEE Circuits Syst. Mag. 56, 58, 60–62 (2009)
E. Gluskin, On one interesting case of the switching nonlinearity. Chaos Solitons Fractals 41, 1870–1872 (2009)
E. Gluskin, Nonlinear sampling and Lebesgue’s integral sums, in Proc. 2010 IEEE 26th Convention of Electrical and Electronics Engineers in Israel, Eilat, Israel, 14–16 Nov. 2010, pp. 00736–00740
E. Gluskin, Some motivating arguments for teaching electrical engineering students. Far East J. Math. Educ. 6(1), 65–80 (2011). http://pphmj.com/journals/fjme.htm
D. Liberzon, Switching in Systems and Control (Birkhauser, Boston, 2003)
X. Liu, K.-L. Teo, H. Zhang, G. Chen, Switching control of linear systems for generating chaos. Chaos Solitons Fractals 30, 725–733 (2006)
M. Margaliot, Stability analysis of switched systems using variational principles: an introduction. Automatica 42, 2059–2077 (2006)
V. Utkin, Sliding Modes in Control and Optimization (Springer, New York, 1992)
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Gluskin, E. An Application of Physical Units (Dimensional) Analysis to the Consideration of Nonlinearity in Electrical Switched Circuits. Circuits Syst Signal Process 31, 737–752 (2012). https://doi.org/10.1007/s00034-011-9324-7
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DOI: https://doi.org/10.1007/s00034-011-9324-7