Abstract
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.
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
Preview
Unable to display preview. Download preview PDF.
References
Probability
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.
Chow, Y. S. and Teicher, H. (1978) Probability Theory: Independence Interchangeably, Martingales, Springer-Verlag, New York.
Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes, Wiley, New York.
Davis, M. H. A. (1977) Linear Estimation and Stochastic Control, Chapman and Hall, London.
Hannan, E. J. (1970) Multiple Time Series, Wiley, New York.
Kingman, J. F. C. and Taylor, S. J. (1966) Introduction to Measure and Probability, Cambridge University Press.
Larson, H. J. (1969) Introduction to Probability Theory and Statistical Inference, Wiley, New York.
Priestley, M. B. (1982) Spectral Analysis and Time Series, Academic Press, London.
Wong, E. (1970) Stochastic Processes in Information and Dynamical Systems, McGraw-Hill, New York.
Linear system theory
Anderson, B. D. O. and Moore, J. B. (1971) Linear Optimal Control, Prentice- Hall, Englewood Cliffs, N.J.
Chen, C. T. (1970) Introduction to Linear System Theory, Holt, Rinehart and Winsten, New York.
Gantmacher, F.R. (1964) The Theory of Matrices, Vols 1 and 2, Chelsea, New York.
Hautus, M. L. J. (1969) Controllability and observability conditions of linear autonomous systems. Ned. Akad. Wetenschappen, Proc. Ser. A, 72 443 - 448.
A simple of proof of Heymann’s lemma. IEEE Trans. Automatic Control, AC-22.
Kailath, T. (1980) Linear Systems, Prentice-Hall, Englewood Cliffs, NJ.
Kalman, R. E. (1960) Contributions to the theory of optimal control. Boletin de la Sociedad Matemática Mexicana, 5, 102 - 119.
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.
Kwakernaak, H. and Slvan, R. Linear Optimal Control Systems, Wiley,New York.
Lang, S. (1979) Linear Algebra ( 2nd edn ), Addison-Wesley, Reading, Mass.
La Salle, J. P. (1960) The time-optimal control problem. In Contributions to Differential Equations, vol. 5, Princeton University Press, Princeton, N.J.
Popov, V. M. (1964) Hyperstability and optimality of automatic systems with several control functions. Rev. Roum. Sci-Electrotechn. et Energ., 9, 629 - 690.
Wilkinson, J. H. (1965) The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.
Wonham, W. M. (1979) Linear Multivariable Control: A Geometric Approach ( 2nd edn ), Springer-Verlag, Berlin.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 M. H. A. Davis and R. B. Vinter
About this chapter
Cite this chapter
Davis, M.H.A., Vinter, R.B. (1985). Probability and linear system theory. In: Stochastic Modelling and Control. Monographs on Statistics and Applied Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4828-0_1
Download citation
DOI: https://doi.org/10.1007/978-94-009-4828-0_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8640-0
Online ISBN: 978-94-009-4828-0
eBook Packages: Springer Book Archive