Simulation of Stiff Hybrid Systems with One-Sided Events and Nonsmooth Boundaries

  • Yury V. ShornikovEmail author
  • Maria S. Nasyrova
  • Dmitry N. Dostovalov
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 343)


Different classes of modal behavior of hybrid systems (HS) are considered. Architecture of instrumental environment is designed in accordance with CSSL standard. Library of original numerical solvers, embedded in simulation environment, is presented. Theorem about the choice of the integration step considering the HS event function dynamic has been formulated and proved. Algorithm of accurate HS event detection with implicit continuous behavior models is designed. Examples of specification and analysis of different hybrid systems models is given.


Computer aided analysis Software architecture Numerical simulation Differential equations Event detection and circuit simulation 



This work was supported by grant 14-01-00047-а from the Russian Foundation for Basic Research, RAS Presidium project № 15.4 “Mathematical modeling, analysis and optimization of hybrid systems”. Yu.V. Shornikov is with the Design Technological Institute of Digital Techniques Siberian Branch of Russian Academy of Science, Novosibirsk, Russia (e-mail: M.S. Myssak, D.N. Dostovalov is with the Department of Automated Control Systems, Novosibirsk State Technical University, Novosibirsk, Russia (e-mails:,


  1. 1.
    Shornikov, Y.V., Tomilov, I.N., Dostovalov, D.N., Denisov, D.N.: Numerical modeling of dynamic processes in electric power systems as a strategic management tool. Scientific Bulletin of the NSTU 4, 129–134 (2011)Google Scholar
  2. 2.
    Novikov, E.A., Shornikov, Y.V.: Computer simulation of stiff hybrid systems: monograph. Publishing house of NSTU, Novosibirsk (2012)Google Scholar
  3. 3.
    Rosenbrock, H.H.: Some general implicit processes for the numerical solution of differential equations. The Computer Journal 5, 329–330 (1963)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Shornikov, Y.V., Dostovalov, D.N., Myssak, M.S.: Simulation of hybrid systems with implicitly specified modal behavior in the ISMA environment. Humanities and Science University Journal 5, 175–182 (2013)Google Scholar
  5. 5.
    Breitenecker, F., Popper, N.: Classification and evaluation of features in advanced simulators. In: MATHMOD, Vienna (2009)Google Scholar
  6. 6.
    Shornikov, Y.V., Druzhinin, V.S., Makarov, N.A., Omelchenko, K.V., Tomilov, I.N.: Official Registration License for Computers 2005610126. Rospatent, Moscow (2005)Google Scholar
  7. 7.
    Shornikov, Y.V., Myssak, M.S., Dostovalov, D.N., Bessonov, A.V.: Using ISMA simulation environment for numerical solution of hybrid systems with PDE. Computer Modeling and Simulation 4, 101–108 (2014)Google Scholar
  8. 8.
    Dostovalov, D.N.: Computer simulation and algorithms of numerical analysis of hybrid systems. Control System and Information Technologies 53(3.1), 128–133 (2013)Google Scholar
  9. 9.
    Shornikov, Y.V., Dostovalov, D.N., Myssak, M.S., et al.: Specification and analysis of discrete behavior of hybrid systems in the workbench ISMA. Open Journal of Applied Sciences. 3(2b), 51–55 (2013)CrossRefGoogle Scholar
  10. 10.
    Arseniev, G.N.: Synthesis and Analysis of Autotracking Systems with Delays in Radio-Electronic Facilities. Information-Measuring Systems 3(2), 25–31 (2005)Google Scholar
  11. 11.
    Oltean, V.E., Dobrescu, R., Popescu, D., Nicolae, M.: On a modal approach for oscillations damping in affine and piecewise affine systems. International Journal of Systems Applications, Engineering & Development 6(1), 1–8 (2012)Google Scholar
  12. 12.
    Popescu, M.-C.O.S., Mastorakis, N.E.: Testing and Simulation of a Motor Vehicle Suspension. International Journal of Systems Applications, Engineering & Development 3(2), 74–83 (2009)Google Scholar
  13. 13.
    Kampowski, W., Rentrop, P., Schmidt, W.: Classication and Numerical Simulation of Electric Circuits. Surveys on Mathematics for Industry 2(1), 23–65 (1992)MathSciNetGoogle Scholar
  14. 14.
    Shornikov, Yu.V., Tomilov, I.N.: The program of language processor from language LISMA. Official registration license for computers № 2007611024. Rospatent, Moscow (2007)Google Scholar
  15. 15.
    De Leeuw, B., Hoogewijs, A.: Statechart normalizations. In: WSEAS Trans. Inf. Sci. Appl. 7(11), 1358–1367 (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yury V. Shornikov
    • 1
    • 2
    Email author
  • Maria S. Nasyrova
    • 1
  • Dmitry N. Dostovalov
    • 1
    • 2
  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Design Technological Institute of Digital Techniques SB RASNovosibirskRussia

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