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5) Consider the following nonlinear system x.1= _x1 +x§ Jf2= —x2+u Using the Lyapunov function V = %xf + ;1‘x§, find the control u that will stabilize this system. 6) Describe step by step (in words) the A* grid-based search algorithm. What are cons of this method? 7) Describe step by step (in words) the Probabilistic Road Map (PRM) sampling-based motion planning method. What are the cons of this method? 8) Describe step by step (in words) the Rapidly-exploring Random Tree (RRT) sampling-based motion planning method. What are the cons of this method?