Mathematical Models of Linear Dynamic Systems and Stochastic Signals

  • Rolf Isermann
  • Marco Münchhof


The main task of identification methods is to derive mathematical models of processes and their signals. Therefore, the most important mathematical models of linear, time-invariant SISO processes as well as stochastic signals shall shortly be presented in the following. It is assumed that the reader is already familiar with timeand frequency domain based models and methods.


Transfer Function Impulse Response Power Spectral Density Order System Step Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Åström KJ (1970) Introduction to stochastic control theory. Academic Press, New YorkzbMATHGoogle Scholar
  2. Åström KJ, Murray RM (2008) Feedback systems: An introduction for scientists and engineers. Princeton University Press, Princeton, NJGoogle Scholar
  3. Box GEP, Jenkins GM, Reinsel GC (2008) Time series analysis: Forecasting and control, 4th edn. Wiley Series in Probability and Statistics, John Wiley, Hoboken, NJzbMATHGoogle Scholar
  4. Bracewell RN (2000) The Fourier transform and its applications, 3rd edn. McGraw-Hill series in electrical and computer engineering, McGraw Hill, BostonGoogle Scholar
  5. Bronstein IN, Semendjajew KA, Musiol G, Mühlig H (2008) Taschenbuch der Mathematik. Harri Deutsch, Frankfurt a. M.zbMATHGoogle Scholar
  6. Chen CT (1999) Linear system theory and design, 3rd edn. Oxford University Press, New YorkGoogle Scholar
  7. Dorf RC, Bishop RH (2008) Modern control systems. Pearson/Prentice Hall, Upper Saddle River, NJGoogle Scholar
  8. Föllinger O (2010) Regelungstechnik: Einführung in die Methoden und ihre Anwendung, 10th edn. Hüthig Verlag, HeidelbergGoogle Scholar
  9. Föllinger O, Kluwe M (2003) Laplace-, Fourier- und ´-Transformationen, 8th edn. Hüthig, HeidelbergGoogle Scholar
  10. Franklin GF, Powell JD, Emami-Naeini A (2009) Feedback control of dynamic systems, 6th edn. Pearson Prentice Hall, Upper Saddle River, NJGoogle Scholar
  11. Franklin GG, Powell DJ, Workmann ML (1998) Digital control of dynamic systems, 3rd edn. Addison-Wesley, Menlo Park, CAGoogle Scholar
  12. Gallager R (1996) Discrete stochastic processes. The Kluwer International Series in Engineering and Computer Science, Kluwer Academic Publishers, BostonGoogle Scholar
  13. Goodwin GC, Sin KS (1984) Adaptive filtering, prediction and control. Prentice-Hall information and system sciences series, Prentice-Hall, Englewood Cliffs, NJzbMATHGoogle Scholar
  14. Goodwin GC, Graebe SF, Salgado ME (2001) Control system design. Prentice Hall, Upper Saddle River NJGoogle Scholar
  15. Grewal MS, Andrews AP (2008) Kalman filtering: Theory and practice using MATLAB, 3rd edn. John Wiley & Sons, Hoboken, NJGoogle Scholar
  16. Hänsler E (2001) Statistische Signale: Grundlagen und Anwendungen. Springer, BerlinzbMATHGoogle Scholar
  17. Heij C, Ran A, Schagen F (2007) Introduction to mathematical systems theory : linear systems, identification and control. Birkhäuser Verlag, BaselzbMATHGoogle Scholar
  18. Isermann R (1991) Digital control systems, 2nd edn. Springer, BerlinGoogle Scholar
  19. Isermann R (1992) Identifikation dynamischer Systeme: Grundlegende Methoden (Vol. 1). Springer, BerlinzbMATHGoogle Scholar
  20. Isermann R (2005) Mechatronic Systems: Fundamentals. Springer, LondonGoogle Scholar
  21. Kammeyer KD, Kroschel K (2009) Digitale Signalverarbeitung: Filterung und Spektralanalyse mit MATLAB-Übungen, 7th edn. Teubner, WiesbadenGoogle Scholar
  22. Ljung L (1999) System identification: Theory for the user, 2nd edn. Prentice Hall Information and System Sciences Series, Prentice Hall PTR, Upper Saddle River, NJGoogle Scholar
  23. Mikleš J, Fikar M (2007) Process modelling, identification, and control. Springer, BerlinzbMATHGoogle Scholar
  24. Moler C, van Loan C (2003) Nineteen dubios ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev 45(1):3–49zbMATHCrossRefMathSciNetGoogle Scholar
  25. Nelles O (2001) Nonlinear system identification: From classical approaches to neural networks and fuzzy models. Springer, BerlinzbMATHGoogle Scholar
  26. Nise NS (2008) Control systems engineering, 5th edn. Wiley, Hoboken, NJGoogle Scholar
  27. Ogata K (2009) Modern control engineering. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  28. Papoulis A (1962) The Fourier integral and its applications. McGraw Hill, New YorkzbMATHGoogle Scholar
  29. Papoulis A, Pillai SU (2002) Probability, random variables and stochastic processes, 4th edn. McGraw Hill, BostonGoogle Scholar
  30. Phillips CL, Nagle HT (1995) Digital control system analysis and design, 3rd edn. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  31. Poularikas AD (1999) The handbook of formulas and tables for signal processing. The Electrical Engineering Handbook Series, CRC Press, Boca Raton, FLGoogle Scholar
  32. Radtke M (1966) Zur Approximation linearer aperiodischer Übergangsfunktionen. Messen, Steuern, Regeln 9:192–196Google Scholar
  33. Söderström T (2002) Discrete-time stochastic systems: Estimation and control, 2nd edn. Advanced Textbooks in Control and Signal Processing, Springer, LondonzbMATHGoogle Scholar
  34. Strejc V (1959) Näherungsverfahren für aperiodische Übergangscharakteristiken. Regelungstechnik 7:124–128zbMATHGoogle Scholar
  35. Verhaegen M, Verdult V (2007) Filtering and system identification: A least squares approach. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  36. Zoubir AM, Iskander RM (2004) Bootstrap Techniques for Signal Processing. Cambridge University Press, Cambridge, UKzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Technische Universität Darmstadt, Institut für AutomatisierungstechnikDarmstadtGermany

Personalised recommendations