QUESTION 7 (6 marks) Time response of a dynamical system x(t) = Ax(t) + Bu(t) can...

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QUESTION 7 (6 marks) Time response of a dynamical system x(t) = Ax(t) + Bu(t) can be obtained by evaluating its solution x(t) = eAtx(0) + e^(t-t) Bu(t)dt, where x(0) is the initial condition and e At = L{(sI A)}. Obtain time response for the following system by finding its solution: where u(t) = 1, and x(0) = [] [8]=[8]+Hu, Use MATLAB to simulate the response of the system to a unit step input with the above initial condition. Comment on the analytical solution and the simulation generated from MATLAB. Determine whether that the system is controllable or not. QUESTION 7 (6 marks) Time response of a dynamical system x(t) = Ax(t) + Bu(t) can be obtained by evaluating its solution x(t) = eAtx(0) + e^(t-t) Bu(t)dt, where x(0) is the initial condition and e At = L{(sI A)}. Obtain time response for the following system by finding its solution: where u(t) = 1, and x(0) = [] [8]=[8]+Hu, Use MATLAB to simulate the response of the system to a unit step input with the above initial condition. Comment on the analytical solution and the simulation generated from MATLAB. Determine whether that the system is controllable or not.