It is known that a given dynamical system has an equilibrium point at the origin. For this system, a function W) has been proposed, and its derivative W() has been computed. Assuming that V(-) and V() are given below you are asked to classify the origin, in each case, as (a) stable, (b) locally uniformly asymptotically stable, and/or (c) globally uniformly asymptotically stable. Explain you answer in each case.
(i) W₁(X,T)= (X²₁ + X²₂), w₁(x,t)=-x²₁