Question

The system is asymptotically stable 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) It is unstable

I got this question in an international level competition.

My question is taken from Liapunov’s Stability Criterion topic in division Liapunov’s Stability Analysis of Control Systems

Answer 1

The correct option is (d) It is unstable

To elaborate: By the definition of Liapunov’s stability criteria the system is asymptotically stable 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 .