Question: Exercise 1: (25 points) Let the following differential equation, parametrized by a with values in R. describe the continuous-time system : :3y(t)27y(t)=u(t)+2u(t),t0 1. Determine the

Exercise 1: (25 points) Let the following differential equation, parametrized by

Exercise 1: (25 points) Let the following differential equation, parametrized by a with values in R. describe the continuous-time system : :3y(t)27y(t)=u(t)+2u(t),t0 1. Determine the transfer function H(s). 2. Give a complete state-model representation for . 3. Draw the corresponding flow diagram. 4. Discuss the stability of for different values of . 5. Discuss controllability and observability for different values of . 6. ** If the system is stabilizable, with a method of your choosing design a state feedback controller K such that the closed-loop system has modes et and tet, with =3

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