# A control theorist looks at abstract nonsense

Introduction

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## Keywords

Category Theory Linear Partial Differential Equation Linear System Theory Infinite Dimensional System Control Fraternity
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## References, with comments

- 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.R. W. Brockett, Finite-Dimensional Linear Systems, John Wiley, 1970.Google Scholar
- 3.R. E. Kalman, P. L. Falb and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, 1969.Google Scholar
- 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.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.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.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.D. G. Tucker, Circuits with Periodically-varying Parameters, Unending Modulators and Parametric Amplifiers, Van Nostrand, 1964.Google Scholar
- 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.S. Ramo, J. R. Whinnery and T. van Duzen, Fields and Waves in Communication Electronics, Wiley, 1965.Google Scholar
- 11.F. R. Gantmakher, Theory of Matrices, 2 vols., Chelsea, 1960.Google Scholar
- 12.R. E. Bellman, Introduction to Matrix Analysis, McGraw-Hill, 1960.Google Scholar
- 13.S. Barnett, Matrices in Control Theory, Van Nostrand, 1971.Google Scholar
- 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.J. L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. Inf. Th. IT-15, 1969, 122–127.CrossRefMathSciNetGoogle Scholar
- 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.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.R. deB. Johnson, Linear systems over various rings, Report ESL-R-497, MIT, 1973.Google Scholar
- 19.B. F. Wyman, Linear systems over rings of operators, this volume.Google Scholar
- 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.B. D. O. Anderson, M. A. Arbib and E. G. Manes, Finitary and infinitary properties in categorical realization theory, to appear.Google Scholar
- 22.L. Schwartz, Théorie des Distributions, 2 vols., Hermann, 1950,51.Google Scholar
- 23.R. W. Newcomb, Linear Multiport Synthesis, McGraw-Hill, 1965.Google Scholar
- 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.E. W. Kamen, On an algebraic representation of continuous-time systemsGoogle Scholar
- 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.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