Consider the following continuous-time state space equation (t) = Ax(t) + Bu(t), y(t) = Cx(t) where 1.5 -1.5 - A = -0.5

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Consider The Following Continuous Time State Space Equation T Ax T Bu T Y T Cx T Where 1 5 1 5 A 0 5 1 (54.17 KiB) Viewed 39 times

Consider the following continuous-time state space equation (t) = Ax(t) + Bu(t), y(t) = Cx(t) where 1.5 -1.5 - A = -0.5 2.5 1 B = and c = [₁ 1], C 0.5 1.5 3 1. Is the system stable? Answer 'Yes' or 'No', and provide a reason. 2. Is the system controllable? Justify your answer by using the PBH rank test. 3. The system uses the state feedback control u = -Kæ. Determine the state feedback gain matrix K such that the closed-loop poles of A - BK are {-2±j, -5}. (Hint: You can use the place command in MATLAB). 4. What is the Act = A - BK matrix for the closed-loop system. 2