Abstract
We consider a class of abstract mathematical models called blocks which generalize some input-output system models which are frequently used in system theory, cybernetics, control theory, signal processing. A block can be described by a multifunction which maps a collection of input signals (input signal bunch) to a non-empty set of collections of output signals (set of output signal bunches). The input and output signal bunches are defined on a subset of a continuous time domain.
We investigate and provide methods for proving the existence of a pair of corresponding input and output signal bunches of a given block, both components of which are defined on the entire time domain (a total input-output pair), and the existence of a total output signal bunch corresponding to a given total input signal bunch.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Baheti, R., Gill, H.: Cyber-physical systems. The Impact of Control Technology, 161–166 (2011)
Lee, E.A., Seshia, S.A.: Introduction to embedded systems: A cyber-physical systems approach (2013), Lulu.com
Shi, J., Wan, J., Yan, H., Suo, H.: A survey of cyber-physical systems. In: 2011 International Conference on Wireless Communications and Signal Processing (WCSP), pp. 1–6. IEEE (2011)
Lee, E.A.: Computing needs time. Communications of the ACM 52, 70–79 (2009)
Oppenheim, A.V., Willsky, A.S., Nawab, S.H.: Signals and systems. Prentice-Hall (1983)
Levine, W.S.: The control handbook. CRC Press (1996)
Zadeh, L.A., Desoer, C.A.: Linear System Theory: The State Space Approach. McGraw-Hill (1963)
Zadeh, L.A.: The concepts of system, aggregate, and state in system theory (1969)
Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory (Pure & Applied Mathematics S.). McGraw-Hill Education (1969)
Padulo, L., Arbib, M.: System theory: a unified state-space approach to continuous and discrete systems. W.B. Saunders Company (1974)
Klir, G.J.: Facets of Systems Science (IFSR International Series on Systems Science and Engineering). Springer (2001)
Wymore, A.W.: A mathematical theory of systems engineering: the elements. Wiley (1967)
Mesarovic, M.D., Takahara, Y.: Abstract Systems Theory. Lecture Notes in Control and Information Sciences. Springer (1989)
Zeigler, B.P., Praehofer, H., Kim, T.G.: Theory of modeling and simulation: integrating discrete event and continuous complex dynamic systems. Academic Press (2000)
Matrosov, V.M., Anapolskiy, L., Vasilyev, S.: The method of comparison in mathematical systems theory. Nauka, Novosibirsk (1980) (in Russian)
Willems, J.C.: Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control 36, 259–294 (1991)
Polderman, J.W., Willems, J.C.: Introduction to mathematical systems theory: a behavioral approach. Springer, Berlin (1997)
Lin, Y.: General systems theory: A mathematical approach. Springer (1999)
Seising, R.: Cybernetics, system(s) theory, information theory and fuzzy sets and systems in the 1950s and 1960s. Information Sciences 180, 4459–4476 (2010)
Goebel, R., Sanfelice, R.G., Teel, A.: Hybrid dynamical systems. IEEE Control Systems 29, 28–93 (2009)
Ball, J.: Finite time blow-up in nonlinear problems. Nonlinear Evolution Equations, pp. 189–205 (1978)
Levine, H.A.: The role of critical exponents in blowup theorems. Siam Review 32, 262–288 (1990)
Goriely, A.: Integrability and nonintegrability of dynamical systems, vol. 19. World Scientific Publishing Company (2001)
Zhang, J., Johansson, K.H., Lygeros, J., Sastry, S.: Zeno hybrid systems. International Journal of Robust and Nonlinear Control 11, 435–451 (2001)
Heymann, M., Lin, F., Meyer, G., Resmerita, S.: Analysis of Zeno behaviors in a class of hybrid systems. IEEE Trans. on Automatic Control 50, 376–383 (2005)
Ivanov, Ie.: An abstract block formalism for engineering systems. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G., Zavileysky, M., Kravtsov, H., Kobets, V., Peschanenko, V.S. (eds.) ICTERI. CEUR Workshop Proceedings, vol. 1000, pp. 448–463. CEUR-WS.org (2013)
Ivanov, Ie.: A criterion for existence of global-in-time trajectories of non-deterministic Markovian systems. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2012. CCIS, vol. 347, pp. 111–130. Springer, Heidelberg (2013)
Nikitchenko, N.S.: A composition nominative approach to program semantics. Technical report, IT-TR 1998-020, Technical University of Denmark (1998)
Hájek, O.: Theory of processes, i. Czechoslovak Mathematical Journal 17, 159–199 (1967)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing
About this paper
Cite this paper
Ivanov, I. (2013). On Existence of Total Input-Output Pairs of Abstract Time Systems. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2013. Communications in Computer and Information Science, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-319-03998-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-03998-5_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03997-8
Online ISBN: 978-3-319-03998-5
eBook Packages: Computer ScienceComputer Science (R0)