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Foundations of system theory: Decomposable systems. (English) Zbl 0294.93002

93B25 Algebraic methods
93Bxx Controllability, observability, and system structure
93A05 Axiomatic systems theory
18B20 Categories of machines, automata
Full Text: DOI
[1] Kalman, R.E.; Falb, P.L.; Arbib, M.A., Topics in mathematical system theory, (1969), McGraw-Hill New York, (See especially Chapter 10.) · Zbl 0231.49001
[2] Arbib, M.A.; Zeiger, H.P., On the relevance of abstract algebra to control theory, Automatica, 5, 589-606, (1969) · Zbl 0199.49303
[3] Goguen, J.A., Minimal realization of machines in closed categories, Bull. am. math. soc, 78, 777-783, (1972) · Zbl 0277.18003
[4] Arbib, M.A.; Manes, E.G., Machines in a category, SIAM review, 16, (1974) · Zbl 0306.18001
[5] Bainbridge, E.S., A unified minimal realization theory, with duality, for machines in a hyperdoctrine, () · Zbl 0327.68057
[6] Brockett, R.W.; Willsky, A.S., Finite-state homomorphic sequential machines, IEEE trans. aut. control, AC-17, 483-490, (1972), (See also the related note by M. A. Arbib in the same issue, pp. 554-555.) · Zbl 0273.93003
[7] Arbib, M.A., Coproducts and group machines, J. comput. syst. sci, 7, 278-287, (1973) · Zbl 0279.94043
[8] Padulo, L.; Arbib, M.A., Deterministic systems: A unified state-variable approach to discrete and continuous systems, (1974), W. B. Saunders Philadelphia · Zbl 0317.93001
[9] Mac Lane, S., Categories for the working Mathematician, (1971), Springer New York · Zbl 0232.18001
[10] Lawvere, F.W., An elementary theory of the category of sets, (), 1506-1511 · Zbl 0141.00603
[11] Lawvere, F.W., Adjointness in foundations, Dialectica, 23, 281-296, (1969), Preprint, to appear · Zbl 0341.18002
[12] Herrlich, H.; Strecker, G.E., Category theory, (1973), Allyn & Bacon Boston · Zbl 0265.18001
[13] \scM. A. Arbib and \scE. G. Manes: Adjoint machines, state-behaviour machines, and duality. J. Pure Appl. Alg., to appear. · Zbl 0323.18002
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