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Observability and Constructibility for Time-Invariant Discrete-Time Systems

In: State Space and Input-Output Linear Systems

Author

Listed:
  • David F. Delchamps

    (Cornell University, School of Electrical Engineering)

Abstract

In this section, we develop the discrete-time analogues of the concepts of observability and constructibility, which were described in §15 for continuous-time systems. Once again, each result has, along with its “abstract” version, a corresponding statement in terms of matrix pairs (A, C). We shall again be referring to the equations xxx $$[\begin{gathered} x\left( {k + 1} \right) = Ax\left( k \right) + Bu\left( k \right),k{\text{2A7E}}{k_o} \hfill \\ x({k_o}) = {x^o} \hfill \\ y(k) = Cx(k) = Du(k), \hfill \\ \end{gathered}$$ and to the time-invariant system with state space R n which they define as in Example 6.6. We begin with a pair of definitions which parallel Definitions 15.1 and 15.2.

Suggested Citation

  • David F. Delchamps, 1998. "Observability and Constructibility for Time-Invariant Discrete-Time Systems," Springer Books, in: State Space and Input-Output Linear Systems, chapter 16, pages 202-207, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3816-4_17
    DOI: 10.1007/978-1-4612-3816-4_17
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