Problem 1 The governing equations of a system are given below: 0 1 x = x+ (1) y = [10] x 1. Determine the poles of the system. Is the system stable or unstable? 2. Is the system controllable? Is it observable? 3. Given u = [13] x + K,r, determine the closed loop poles. 4. Determine the closed-loop transfer function () R(8) 5. Determine the reference gain K, such that the steady state error is zero for a unit step input. HINT: The inverse of a 2x2 matrix is given by: -1 1 = ad-bc C a