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Coalgebraic foundations of linear systems

Published: 20 August 2007 Publication History

Abstract

Viewing discrete-time causal linear systems as (Mealy) coalgebras, we describe their semantics, minimization and realisation as universal constructions, based on the final coalgebras of streams and causal stream functions.

References

[1]
Arbib, M.A., Manes, E.G.: Foundations of system theory: decomposable systems. Automatica 10, 285-302 (1974).
[2]
Arbib, M.A., Manes, E.G.: Adjoint machines, state-behaviour machines, and duality. Journal of Pure and Applied Algebra 6, 313-344 (1975).
[3]
Benveniste, A.: A brief on realisation theory for linear systems (unpublished note).
[4]
Birkhoff, G., MacLane, S.: A survey of modern algebra, 4th edn. MacMillan Publishing Co., Inc. (1977).
[5]
Eilenberg, S.: Automata, languages and machines. In: Pure and applied mathematics, vol. A, Academic Press, London (1974).
[6]
Fuhrmann, P.A.: A polynomial approach to linear algebra. Springer, Berlin (1996).
[7]
Hansen, H., Costa, D., Rutten, J.J.M.M.: Synthesis of Mealy machines using derivatives. In: Proceedings of CMCS 2006. ENTCS, vol. 164(1), pp. 27-45. Elsevier, Amsterdam (2006).
[8]
Kailath, T.: Linear systems. Prentice-Hall, Englewood Cliffs (1980).
[9]
Kalman, R.E.: Mathematical description of linear dynamical systems. SIAM J. Control 1, 152-192 (1963).
[10]
Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in mathematical system theory. McGraw-Hill, New York (1969).
[11]
Kohavi, Z.: Switching and finite automata theory. McGraw-Hill, New York (1978).
[12]
Lahti, B.P.: Signal Processing & Linear Systems. Oxford University Press, Oxford (1998).
[13]
Pappas, G.J.: Bisimilar linear systems. Automatica 39, 2035-2047 (2003).
[14]
Rutten, J.J.M.M.: Behavioural differential equations: a coinductive calculus of streams, automata, and power series (Fundamental Study). Theoretical Computer Science 308(1), 1-53 (2003).
[15]
Rutten, J.J.M.M.: A tutorial on coinductive stream calculus and signal flow graphs. Theoretical Computer Science 343(3), 443-481 (2005).
[16]
Rutten, J.J.M.M.: Algebraic specification and coalgebraic synthesis of Mealy automata. In: Proceedings of FACS 2005. ENTCS, vol. 160, pp. 305-319. Elsevier Science Publishers, Amsterdam (2006).
[17]
Sontag, E.D.: Polynomial response maps. Lecture Notes in Control and Information Sciences, vol. 13. Springer, Heidelberg (1979).
[18]
van der Schaft, A.J.: Equivalence of dynamical systems by bisimulation. IEEE Transactions on Automatic Control 49, 2160-2172 (2004).

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  • (2008)Calculating Invariants as Coreflexive BisimulationsProceedings of the 12th international conference on Algebraic Methodology and Software Technology10.1007/978-3-540-79980-1_7(83-99)Online publication date: 28-Jul-2008
  1. Coalgebraic foundations of linear systems

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    cover image Guide Proceedings
    CALCO'07: Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
    August 2007
    462 pages
    ISBN:9783540738572
    • Editors:
    • Till Mossakowski,
    • Ugo Montanari,
    • Magne Haveraaen

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    Springer-Verlag

    Berlin, Heidelberg

    Publication History

    Published: 20 August 2007

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    • (2008)Calculating Invariants as Coreflexive BisimulationsProceedings of the 12th international conference on Algebraic Methodology and Software Technology10.1007/978-3-540-79980-1_7(83-99)Online publication date: 28-Jul-2008

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