Question

A system is said to be locally stable if:

(a) The region S (e) is small

(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) They are unstable

I have been asked this question in semester exam.

The question is from Liapunov’s Stability Criterion in section Liapunov’s Stability Analysis of Control Systems

Answer 1

Right answer is (a) The region S (e) is small

Explanation: By the definition of Liapunov’s stability criteria a system is locally stable if the region of system is very small.