Question

The system is unstable for:

(a) W (x)>0; x not equal to zero

(b) W (0) =0

(c) W (x) has continuous partial derivative with respect to all components of x

(d) All of the mentioned

This question was addressed to me in an international level competition.

The doubt is from The Direct Method and  Constructing of Liapunov for the Linear and Non-Linear System in division Liapunov’s Stability Analysis of Control Systems

Answer 1

Right option is (d) All of the mentioned

Explanation: It requires much ingenuity of devise a suitable W function to devise a Liapunov function V. In stability analysis of nonlinear systems, it is valuable to establish conditions for which the system is unstable.