A control theorist looks at abstract nonsense

  • B. D. O. Anderson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 25)


Category Theory Linear Partial Differential Equation Linear System Theory Infinite Dimensional System Control Fraternity 
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.


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References, with comments

  1. 1.
    C. A. Desoer and E. S. Kuh, Basic Circuit Theory, McGraw-Hill, 1970. (This text is valuable for various linear systems viewpoints, all within the framework of networks. The sorts of network descriptions used include ordinary differential equations like (1), state-variable systems like (2), impulse response description (related to (4)) and Laplace transform and Fourier transform descriptions. The latter two, though differing but trivially from the mathematical viewpoint in many cases, provide to an engineer vastly differing heuristically derived information.)Google Scholar
  2. 2.
    R. W. Brockett, Finite-Dimensional Linear Systems, John Wiley, 1970.Google Scholar
  3. 3.
    R. E. Kalman, P. L. Falb and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, 1969.Google Scholar
  4. 4.
    B. D. O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis; A Modern Systems Theory Approach, Prentice Hall, 1973. (This text discusses network theory almost exclusively using state-variable ideas. It contains a one chapter survey of many results concerning finite-dimensional linear systems).Google Scholar
  5. 5.
    B. D. O. Anderson and J. B. Moore, Linear Optimal Control, Prentice-Hall, 1971. (This book contains a discussion of observers, both in a deterministic framework and a stochastic framework —the latter because one needs to model and cope with the effects of measurement noise picked up by the sensors associated with a physical linear system.)Google Scholar
  6. 6.
    L. A. Zadeh and C. A. Desoer, Linear System Theory-A State Space Approach, McGraw-Hill, 1963. (This book was the first to present system theory in a form that engineers could understand. It is a source of many valuable ideas.)Google Scholar
  7. 7.
    R. R. Mohler and A. Ruberti, eds., Theory and Application of Variable Structure Systems, Academic Press, 1972. (This book is a collection of papers, some offering examples of nonlinear systems).Google Scholar
  8. 8.
    D. G. Tucker, Circuits with Periodically-varying Parameters, Unending Modulators and Parametric Amplifiers, Van Nostrand, 1964.Google Scholar
  9. 9.
    M. Athans and P. L. Falb, Optimal Control, McGraw-Hill, 1966. (This book has a fairly lengthy introduction to linear systems theory before entering on a discussion of optimal control theory).Google Scholar
  10. 10.
    S. Ramo, J. R. Whinnery and T. van Duzen, Fields and Waves in Communication Electronics, Wiley, 1965.Google Scholar
  11. 11.
    F. R. Gantmakher, Theory of Matrices, 2 vols., Chelsea, 1960.Google Scholar
  12. 12.
    R. E. Bellman, Introduction to Matrix Analysis, McGraw-Hill, 1960.Google Scholar
  13. 13.
    S. Barnett, Matrices in Control Theory, Van Nostrand, 1971.Google Scholar
  14. 14.
    M. A. Arbib and E. G. Manes, Foundations of system theory: decomposable machines, Automatica, to appear. (This is an interesting paper, providing a better unification of some results of linear systems and group machines then hitherto available. Whether the approach will catch on with the control fraternity or not may well depend on what the contents of sequel papers are).Google Scholar
  15. 15.
    J. L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. Inf. Th. IT-15, 1969, 122–127.CrossRefMathSciNetGoogle Scholar
  16. 16.
    Y. Rouchaleau, B. F. Wyman and R. E. Kalman, Algebraic structure of linear dynamical systems, III: realization theory over a commutative ring, Proc. Nat. Acad. Sci. 69, 1972, 3404–3406.CrossRefMathSciNetGoogle Scholar
  17. 17.
    R. W. Brockett and J. L. Willems, Systems defined on modules and applications to the control of linear partial differential equations, Automatica, to appear.Google Scholar
  18. 18.
    R. deB. Johnson, Linear systems over various rings, Report ESL-R-497, MIT, 1973.Google Scholar
  19. 19.
    B. F. Wyman, Linear systems over rings of operators, this volume.Google Scholar
  20. 20.
    R. W. Brockett and A. S. Willsky, Finite state homomorphic sequential machines, IEEE Trans. Auto. Cont. AC-17, 1973, 483–490.MathSciNetGoogle Scholar
  21. 21.
    B. D. O. Anderson, M. A. Arbib and E. G. Manes, Finitary and infinitary properties in categorical realization theory, to appear.Google Scholar
  22. 22.
    L. Schwartz, Théorie des Distributions, 2 vols., Hermann, 1950,51.Google Scholar
  23. 23.
    R. W. Newcomb, Linear Multiport Synthesis, McGraw-Hill, 1965.Google Scholar
  24. 24.
    R. E. Kalman and M. L. J. Hautus, Realization of continuous-time linear dynamical systems: rigorous theory in the style of Schwartz, Proc. NRL Conf. on Differential Equations, 1971.Google Scholar
  25. 25.
    E. W. Kamen, On an algebraic representation of continuous-time systemsGoogle Scholar
  26. 26.
    M. R. Wohlers, Lumped and Distributed Passive Networks, Academic Press, 1969. (See also issues of the IEEE Transactions on Circuit Theory for material on lumped-distributed systems).Google Scholar
  27. 27.
    E. W. Kamen, Control of linear continuous-time systems defined over rings of distributions, this volume.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • B. D. O. Anderson
    • 1
  1. 1.Electrical EngineeringUniversity of NewcastleNSWAustralia

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