Definition For Discrete-time Systems
The definition for discrete-time systems is almost identical to that for continuous-time systems. The definition below provides this, using an alternate language commonly used in more mathematical texts.
Let be a metric space and a continuous function. A point is said to be Lyapunov stable, if, for each, there is a such that for all, if
then
for all .
We say that is asymptotically stable if it belongs to the interior of its stable set, i.e. if there is a such that
whenever .
Read more about this topic: Lyapunov Stability
Famous quotes containing the words definition and/or systems:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Before anything else, we need a new age of Enlightenment. Our present political systems must relinquish their claims on truth, justice and freedom and have to replace them with the search for truth, justice, freedom and reason.”
—Friedrich Dürrenmatt (1921–1990)