

1 For each of the following systems 

a) show 

 EMBED Equation  

		is a Lyapunov function for the system.

b) show  EMBED Equation  is an equilibrium point of the system.

c) show  EMBED Equation  is a stationary point for  EMBED Equation  

d) determine the type of stationary point  by looking at the eigenvalues of the Hessian matrix

e) determine the stability of the equilibrium point.



  	A)    EMBED Equation  	 EMBED Equation  

	  B)    EMBED Equation  	 EMBED Equation  

  C)    EMBED Equation  	 EMBED Equation  	

     

2 Repeat question (1) for

 EMBED Equation  

and the following systems

	a)    EMBED Equation  	 EMBED Equation  

b)    EMBED Equation  	 EMBED Equation  



3 Show that the system

 EMBED Equation  

has no closed orbits by construsting a Lyapunov function 

 EMBED Equation  

with suitable a and b.



