Probability and linear system theory

  • M. H. A. Davis
  • R. B. Vinter
Part of the Monographs on Statistics and Applied Probability book series (MSAP)


This book is concerned with the analysis of discrete-time linear systems subject to random disturbances. This introductory chapter is designed to present the main results in the two areas of probability and linear systems theory as required for the main developments of the book, beginning in Chapter 2.


Random Vector Covariance Function Input Sequence Cauchy Sequence Spectral Density Function 
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. Bartle, R. G. (1964) The Elements of Real Analysis, John Wiley, New York. Chatfield, C. (1979) The Analysis of Time Series: Theory and Practice ( 2nd edn ), Chapman and Hall, London.Google Scholar
  2. Chow, Y. S. and Teicher, H. (1978) Probability Theory: Independence Interchangeably, Martingales, Springer-Verlag, New York.Google Scholar
  3. Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes, Wiley, New York.Google Scholar
  4. Davis, M. H. A. (1977) Linear Estimation and Stochastic Control, Chapman and Hall, London.Google Scholar
  5. Hannan, E. J. (1970) Multiple Time Series, Wiley, New York.CrossRefGoogle Scholar
  6. Kingman, J. F. C. and Taylor, S. J. (1966) Introduction to Measure and Probability, Cambridge University Press.CrossRefGoogle Scholar
  7. Larson, H. J. (1969) Introduction to Probability Theory and Statistical Inference, Wiley, New York.Google Scholar
  8. Priestley, M. B. (1982) Spectral Analysis and Time Series, Academic Press, London.Google Scholar
  9. Wong, E. (1970) Stochastic Processes in Information and Dynamical Systems, McGraw-Hill, New York.Google Scholar

Linear system theory

  1. Anderson, B. D. O. and Moore, J. B. (1971) Linear Optimal Control, Prentice- Hall, Englewood Cliffs, N.J.Google Scholar
  2. Chen, C. T. (1970) Introduction to Linear System Theory, Holt, Rinehart and Winsten, New York.Google Scholar
  3. Gantmacher, F.R. (1964) The Theory of Matrices, Vols 1 and 2, Chelsea, New York.Google Scholar
  4. Hautus, M. L. J. (1969) Controllability and observability conditions of linear autonomous systems. Ned. Akad. Wetenschappen, Proc. Ser. A, 72 443 - 448.Google Scholar
  5. A simple of proof of Heymann’s lemma. IEEE Trans. Automatic Control, AC-22.Google Scholar
  6. Kailath, T. (1980) Linear Systems, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  7. Kalman, R. E. (1960) Contributions to the theory of optimal control. Boletin de la Sociedad Matemática Mexicana, 5, 102 - 119.Google Scholar
  8. Kalman, R. E., Ho, Y. C. and Narendra, K. S. (1963) Controllability of linear dynamical systems. In Contributions to the Theory of Differential Equations, vol. 1, Wiley-Interscience, New York.Google Scholar
  9. Kwakernaak, H. and Slvan, R. Linear Optimal Control Systems, Wiley,New York.Google Scholar
  10. Lang, S. (1979) Linear Algebra ( 2nd edn ), Addison-Wesley, Reading, Mass.Google Scholar
  11. La Salle, J. P. (1960) The time-optimal control problem. In Contributions to Differential Equations, vol. 5, Princeton University Press, Princeton, N.J.Google Scholar
  12. Popov, V. M. (1964) Hyperstability and optimality of automatic systems with several control functions. Rev. Roum. Sci-Electrotechn. et Energ., 9, 629 - 690.Google Scholar
  13. Wilkinson, J. H. (1965) The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.Google Scholar
  14. Wonham, W. M. (1979) Linear Multivariable Control: A Geometric Approach ( 2nd edn ), Springer-Verlag, Berlin.Google Scholar

Copyright information

© M. H. A. Davis and R. B. Vinter 1985

Authors and Affiliations

  • M. H. A. Davis
    • 1
  • R. B. Vinter
    • 1
  1. 1.Department of Electrical EngineeringImperial CollegeLondonUK

Personalised recommendations