A plant can be described by -n(t) ra(t) + z3(t) + u(t) (t) 12(t) r2() and let the control law be u(t) = 07 (t) 23(6) - (201(t) + 33(t)) (a) [6p] Show that r = 0 is a global asymptotically stable equilibrium point for t closed loop system. (Hint: Use V(r) = 2* +53 +503 +2113 (b) [4p] In order to evaluate the gain margin of the closed loop system, study the contr u(t) = A (101(t) 23(t) (261(t) + 23(t)) where Am > 0 is a gain. Decide for which Am the closed loop system is stab or unstable. (Hint: Study the stability properties of the linearized closed loop system. law A plant can be described by -n(t) ra(t) + z3(t) + u(t) (t) 12(t) r2() and let the control law be u(t) = 07 (t) 23(6) - (201(t) + 33(t)) (a) [6p] Show that r = 0 is a global asymptotically stable equilibrium point for t closed loop system. (Hint: Use V(r) = 2* +53 +503 +2113 (b) [4p] In order to evaluate the gain margin of the closed loop system, study the contr u(t) = A (101(t) 23(t) (261(t) + 23(t)) where Am > 0 is a gain. Decide for which Am the closed loop system is stab or unstable. (Hint: Study the stability properties of the linearized closed loop system. law