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External Dynamical Equivalence of Analytic Control Systems

In: Mathematical Control Theory and Finance

Author

Listed:
  • Zbigniew Bartosiewicz

    (Białystok Technical University, Faculty of Computer Sciences)

  • Ewa Pawłuszewicz

    (Białystok Technical University, Faculty of Computer Sciences)

Abstract

Summary Theory of systems on homogeneous time scales unifies theories of continuous-time and discrete-time systems. The characterizations of external dynamical equivalence known for continuous-time and discrete-time systems are extended here to systems on time scales. Under assumption of uniform observability, it is shown that two analytic control systems with output are externally dynamically equivalent if and only if their delta universes are isomorphic. The delta operator associated to the system on a time scale is a generalization of the differential operator associated to a continuous-time system and of the difference operator associated to a discrete-time system.

Suggested Citation

  • Zbigniew Bartosiewicz & Ewa Pawłuszewicz, 2008. "External Dynamical Equivalence of Analytic Control Systems," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 55-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_4
    DOI: 10.1007/978-3-540-69532-5_4
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