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:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“The only people who treasure systems are those whom the whole truth evades, who want to catch it by the tail. A system is just like truth’s tail, but the truth is like a lizard. It will leave the tail in your hand and escape; it knows that it will soon grow another tail.”
—Ivan Sergeevich Turgenev (1818–1883)