Let V(x , y) = A + B , where A and B are constant real numbers, be a Liapunov function in a domain D (containing the fixed point at the origin) for the autonomous non-linear system .Find A and B if the derivative of V along the trajectories of the system is equal to - .Is the origin stable, asymptotically stable, or unstable?
A) A = 2, B = -3; asymptotically stable
B) A = -2, B = -3; unstable
C) A =2, B = 3; unstable
D) A = -2, B = 3; stable
E) A = 2, B = 3; asymptotically stable

Question

Let V(x , y) = A  + B  , where A and B are constant real numbers, be a Liapunov function in a domain D (containing the fixed point at the origin) for the autonomous non-linear system  .Find A and B if the derivative of V along the trajectories of the system is equal to -  .Is the origin stable, asymptotically stable, or unstable?
A) A = 2, B = -3; asymptotically stable 
B) A = -2, B = -3; unstable 
C) A =2, B = 3; unstable 
D) A = -2, B = 3; stable 
E) A = 2, B = 3; asymptotically stable

Quizplus · Accepted Answer

The Answer of Let V(x , y) = A  + B  , where A and B are constant real numbers, be a Liapunov function in a domain D (containing the fixed point at the origin) for the autonomous non-linear system  .Find A and B if the derivative of V along the trajectories of the system is equal to -  .Is the origin stable, asymptotically stable, or unstable?
A) A = 2, B = -3; asymptotically stable 
B) A = -2, B = -3; unstable 
C) A =2, B = 3; unstable 
D) A = -2, B = 3; stable 
E) A = 2, B = 3; asymptotically stable

Let V(x , Y) = a + B