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


MSC:

93B25 Algebraic methods
93Bxx Controllability, observability, and system structure
93A05 Axiomatic systems theory
18B20 Categories of machines, automata
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[1] Kalman, R. E.; Falb, P. L.; Arbib, M. A., Topics in Mathematical System Theory (1969), McGraw-Hill: 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, (Ph.D. Dissertation (1973), University of Michigan) · 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: W. B. Saunders Philadelphia · Zbl 0317.93001
[9] Mac Lane, S., Categories for the Working Mathematician (1971), Springer: Springer New York · Zbl 0232.18001
[10] Lawvere, F. W., An elementary theory of the category of sets, (Proc. Natn. Acad. Sci. U.S.A, 52 (1964)), 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: Allyn & Bacon Boston · Zbl 0265.18001
[13] M. A. ArbibE. G. ManesJ. Pure Appl. Alg.; M. A. ArbibE. G. ManesJ. Pure Appl. Alg. · Zbl 0323.18002
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