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Reachability and Controllability for Time-Invariant Continuous-Time Systems

In: State Space and Input-Output Linear Systems

Author

Listed:
  • David F. Delchamps

    (Cornell University, School of Electrical Engineering)

Abstract

It is worthwhile at this point to look back at the six previous sections and determine the roles they play in our study of state space linear systems. In §6, we presented a formal definition of state space linear system; such a system is a composite mathematical object with various components: the space U of m -vector input functions, the spaces $${Y_{{t_o}}}$$ of p -vector output functions, the (finite-dimensional) state space X, the state transition mapping φ, and the readout mapping ρ. Fundamental examples of linear systems were given in Examples 6.5 and 6.6; in §7, it was shown that an understanding of these examples leads in an essential way to a deep understanding of “almost all” finite-dimensional state space linear systems. The principle underlying the development in §7 is that realizations may be constructed for “most” continuous-time systems and all discrete-time systems; the crucial step in the realization process is a choice of basis for the state space X

Suggested Citation

  • David F. Delchamps, 1998. "Reachability and Controllability for Time-Invariant Continuous-Time Systems," Springer Books, in: State Space and Input-Output Linear Systems, chapter 13, pages 176-186, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3816-4_14
    DOI: 10.1007/978-1-4612-3816-4_14
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