DO NOT TURN THIS HOMEWORK IN!!

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

b) Determine the equilibrium points of:

i)

ii)

2a) In class we learned that we could apply Lyapunov stability theory to discrete systems,

where we should still choose:

We also said that we should replace any by a first difference

Let's now consider the linear discrete system given by:

Following the procedure we developed for continuous linear systems, show that the Lyapunov equation reduces to:

where

b) Use the above result and Lyanuov stability theory to determine the stability of:

(use Q = identity matrix)