A “stochastic system” is understood here as a dynamic system that has some kind of uncertainty. The type of uncertainty will be specified in a precise mathematical sense when dealing with methods of analysis and design. At this point, it is sufficient to say that the uncertainty will include disturbances acting on the system, sensor errors and other measurement errors, as well as partly unknown dynamics of the system. The uncertainties will be modelled in a probabilistic way using random variables and stochastic processes as important tools.


Transmitted Signal Stochastic System Radio Communication Sensor Error Electric Power Consumption 
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  1. There is a huge literature on stochastic dynamic systems. for some alternative books on estimation and control, see, for exmaple: Anderson, B.D.O., Moore, J.B., 1979. Optimal Filtering. Prentice Hall, Englewood Cliffs, NJ.MATHGoogle Scholar
  2. Åström, K.J., 1970. Introduction to Stochastic Control. Academic Press, New York.MATHGoogle Scholar
  3. Borrie, J.A., 1992. Stochastic Systems for Engineers. Prentice Hall International, Hemel Hempstead, UK.MATHGoogle Scholar
  4. Brown, R.G., 1983. Introduction to Random Signal Analysis and Kaiman Filtering. John Wiley & Sons, New York.Google Scholar
  5. Grimble, M.J., Johnson, M.A., 1988. Optimal Control and Stochastic Estimation, vol. 2., John Wiley & Sons, Chichester.Google Scholar
  6. Jazwinski, A.H., 1970. Stochastic Processes and Filtering Theory. Academic Press, New York.MATHGoogle Scholar
  7. Kailath, T., Sayed, A.H., Hassibi, B., 2000. Linear Estimation. Prentice Hall, Upper Saddle River, NJ.Google Scholar
  8. Lewis, F.L., 1986. Optimal Estimation. John Wiley & Sons, New York.MATHGoogle Scholar
  9. Maybeck, P.S., 1979–1982. Stochastic Models, Estimation and Control, vols 1–3. Academic Press, New York.Google Scholar
  10. Needless to say, there are also many books dedicated to stochastic processes in general. for some collections of historial key papers on estimation of stochastic systems, see: Kailath, T. (Ed.), 1977. Linear Least-Squares Estimation. Dowden, Hutchinson and Ross, Inc., Stroudsburg, PA.Google Scholar
  11. Sorenson, H. (Ed.), 1985. Kalman Filtering: Theory and Application. IEEE Press, New York.Google Scholar
  12. This book deals with analysis and design for given stochastic models. To build (or estimate) dynamic models from experimental data is called system identification. for some general texts on that subject, see: Ljung, L., 1999. Identification — Theory for the User, second ed. Prentice Hall, Upper Saddle River, NJ.Google Scholar
  13. Söderström, T., Stoica, P., 1989. System Identification. Prentice Hall International, Hemel Hempstead, UK.Google Scholar

Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • T. Söderström
    • 1
  1. 1.Department of Systems and Control, Information TechnologyUppsala UniversityUppsalaSweden

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