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State Space Linear Systems: Formal Definitions and General Properties

In: State Space and Input-Output Linear Systems

Author

Listed:
  • David F. Delchamps

    (Cornell University, School of Electrical Engineering)

Abstract

In this section, we present formal definitions of continuous-and discrete-time state space linear systems and discuss some general properties which such systems exhibit. The treatment may be viewed as an effort to make precise some of the notions described heuristically in the Introduction. Specifically, linear systems should serve as mathematical models for “real-world” processes which take input “time functions” to output “time functions” in some linear fashion. The real-world processes which we seek to model with, say, continuous-time state space linear systems are those which take m real-valued suitably well-behaved input time-functions t →u i (t), 1 ⩽ i ⩽ m, and “process” them through a box in such a way as to yield p real-valued output time functions t →y j (t), 1 ⩽ j ⩽ p.

Suggested Citation

  • David F. Delchamps, 1998. "State Space Linear Systems: Formal Definitions and General Properties," Springer Books, in: State Space and Input-Output Linear Systems, chapter 6, pages 89-103, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3816-4_7
    DOI: 10.1007/978-1-4612-3816-4_7
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