2. Consider the following state-space system representation. dz dt = 0 10] 0 01 Z+0 u...

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2. Consider the following state-space system representation. dz dt = 0 10] 0 01 Z+0 u -2 3 5 y=[100]z a) Determine if the system is controllable. b) If so, find its controllable canonical form. c) Determine the coordinate transform * = Tx for the controllable canonical system. d) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -3, and -7. e) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -2+5j. 2. Consider the following state-space system representation. dz dt = 0 10] 0 01 Z+0 u -2 3 5 y=[100]z a) Determine if the system is controllable. b) If so, find its controllable canonical form. c) Determine the coordinate transform * = Tx for the controllable canonical system. d) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -3, and -7. e) Use the formulations of the characteristic equation to determine the gain matrix K for a controller producing the system dynamics with eigenvalues of -1, -2+5j.