Question

The system is asymptotically stable in the large at the origin if :

(a) It is stable

(b) There exist a real number >0 such that || x (t0) || <=r

(c) Every initial state x (t0) results in x (t) tends to zero as t tends to infinity

(d) Both a and c

The question was posed to me in homework.

Origin of the question is Liapunov’s Stability Criterion in chapter Liapunov’s Stability Analysis of Control Systems

Answer 1

Right option is (d) Both a and c

Explanation: By the definition of Liapunov’s stability criteria the system is asymptotically stable in the large at the origin if there exist a real number >0 such that || x (t0) || <=r and every initial state x (t0) results in x (t) tends to zero as t tends to infinity.