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
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