Top 30 analogous words or synonyms for asymptotic
Article | Example |
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ଲ୍ୟାପୁନୋଭ୍ ସ୍ଥାୟୀତ୍ତ୍ଵ | Usually, it is difficult to analyze the "asymptotic" stability of time-varying systems because it is very difficult to find Lyapunov functions with a "negative definite" derivative. |
ଲ୍ୟାପୁନୋଭ୍ ସ୍ଥାୟୀତ୍ତ୍ଵ | It seems that if the parameter formula_65 is positive, stability is asymptotic for formula_66 But this is wrong, since formula_67 does not depend on formula_68, and will be 0 everywhere on the formula_68 axis. The system is Lyapunov stable. |
ଲ୍ୟାପୁନୋଭ୍ ସ୍ଥାୟୀତ୍ତ୍ଵ | We know that in case of autonomous (time-invariant) systems, if formula_88 is negative semi-definite (NSD), then also, it is possible to know the asymptotic behaviour by invoking invariant-set theorems. However, this flexibility is not available for "time-varying" systems. |
ଲ୍ୟାପୁନୋଭ୍ ସ୍ଥାୟୀତ୍ତ୍ଵ | That is, if "x" belongs to the interior of its stable manifold, it is "asymptotically stable" if it is both attractive and stable. (There are counterexamples showing that attractivity does not imply asymptotic stability. Such examples are easy to create using homoclinic connections.) |
ଲ୍ୟାପୁନୋଭ୍ ସ୍ଥାୟୀତ୍ତ୍ଵ | Then "V(x)" is called a Lyapunov function candidate and the system is stable in the sense of Lyapunov. (Note that formula_40 is required; otherwise for example formula_41 would "prove" that formula_42 is locally stable. An additional condition called "properness" or "radial unboundedness" is required in order to conclude global stability.) Furthermore, the system is asymptotically stable, in the sense of Lyapunov, if formula_43 with equality if and only if formula_36. Global asymptotic stability (GAS) follows similarly. |