Do NOT TURN THIS HOMEWORK IN!!

1a) Use Krasovskii's Method to determine the stability of the origin if:

This is negative semi-definite, so system is ISL stable

b) Determine the equilibrium points of:

i)

ii)

These equations conflict!! Therefore, no equilibrium points!!

2a)

b) Use Lyanuov stability theory to determine the stability of:

Therefore, P is positive definite, and the system is asymptotically stable!!