Abstract
The paper is devoted to the analysis of a class of mathematical models containing small parameters, namely—singularly perturbed state models. These models are of special interest for the researchers, who deal with computer simulation because the models reflect distinctive properties of the object under consideration, which should be taken into account in the practical design. Specifically, under proper conditions, small variations of parameters may cause substantial changes in physical states of the actual object. Using electronic circuits as examples, structural conditions are studied, which cause the availability of singularly perturbed state models presented in the form of the set of ordinary differential equations with small parameters on derivatives of state variables. It is suggested that the proposed approach to the structural analysis of the mentioned type of mathematical models can be extended to other classes of engineering objects by invoking the well-known principle of physical analogies.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hadamard, J.: Sur les problèmes aux dérivées partielles et leur signification physique. Princeton Univ. Bull. 13, 49–52 (1902)
DeRusso, P.M., Roy, R.J., Close, C.M., Desrochers, A.D.: State Variables for Engineers. Wiley, New York (1997)
Desoer, C., Kuh, E.: Basic Circuit Theory. McGraw-Hill, New York (1969)
Sommariva, A.M.: State-space equations of regular and strictly topologically degenerate linear lumped time-invariant networks: the multiport method. Int. J. Circuit Theory Appl. 29, 435–453 (2001)
Riaza, R.: Differential-Algebraic Systems: Analytical Aspects and Circuit Applications. World Scientific Publishing, Singapore (2008)
Vlach, J.: Linear Circuit Theory: Matrices in Computer Applications. Apple Academic Press, Toronto (2014)
Kadalbajo, M.K., Patiodar, K.C.: A survey of numerical techniques for solving singularly-perturbed ordinary differential equations. Appl. Math. Comput. 130, 457–510 (2002)
Huelsman, L.P.: Active and Passive Analog Filter Design. An Introduction, p. 480. McGraw-Hill Co., New York (1993)
Tikhonov, A.N.: Systems of differential equations containing a small parameter multiplying the derivative. (in Russian). Mat. Sb. 31(73), 575–586 (1952)
Brugnano, L., Trigiante, D.: On the characterization of stiffness for ODEs. Dynam. Contin. Discrete Impulse Syst. 2(3), 327–335 (1996)
Ferry, D.K., Akers, L.A., Greeneich, E.W.: Ultra Large Scale Integrated Microelectronics, p. 316. Prentice Hall, Englewood Cliffs (1988)
Rogoza, W.: Adaptive simulation of separable dynamical systems in the neural network basis. In: Pejas, J., Piegat, A. (eds.) Enhanced Methods in Computer Security, Biometric and Artificial Intelligence Systems, pp. 371–386. Springer, New York (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rogoza, W. (2015). Structural Analysis of Singularly Perturbed State Models. In: Wiliński, A., Fray, I., Pejaś, J. (eds) Soft Computing in Computer and Information Science. Advances in Intelligent Systems and Computing, vol 342. Springer, Cham. https://doi.org/10.1007/978-3-319-15147-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-319-15147-2_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15146-5
Online ISBN: 978-3-319-15147-2
eBook Packages: EngineeringEngineering (R0)