Step Response - Formal Mathematical Description

Formal Mathematical Description

This section provides a formal mathematical definition of step response in terms of the abstract mathematical concept of a dynamical system : all notations and assumptions required for the following description are listed here.

  • is the evolution parameter of the system, called "time" for the sake of simplicity,
  • is the state of the system at time, called "output" for the sake of simplicity,
  • is the dynamical system evolution function,
  • is the dynamical system initial state,
  • is the Heaviside step function

Read more about this topic:  Step Response

Famous quotes containing the words formal, mathematical and/or description:

    There must be a profound recognition that parents are the first teachers and that education begins before formal schooling and is deeply rooted in the values, traditions, and norms of family and culture.
    Sara Lawrence Lightfoot (20th century)

    All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
    Roger Bacon (c. 1214–c. 1294)

    As they are not seen on their way down the streams, it is thought by fishermen that they never return, but waste away and die, clinging to rocks and stumps of trees for an indefinite period; a tragic feature in the scenery of the river bottoms worthy to be remembered with Shakespeare’s description of the sea-floor.
    Henry David Thoreau (1817–1862)