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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. Its no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (18901960)
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Pauls, like the editions of Balbec and Palmyra.”
—Horace Walpole (17171797)