H.W: Consider a system described by the following state space form: [x; x2 ] = [0 10 1][*, X2] + [[ 1 ]u y = [10][* x2] The performance index is given by: J = (x[1 001 ]x + u?) dt J } " ]+ 0 Determine the LQR gain matrix analytical and by using Matlab software and then implement the LQR controller system using Matlab/Simulink and finally, compare the results obtained from Matlab script and Simulink model. H.W: Consider a system described by the following state space form: [x; x2 ] = [0 10 1][*, X2] + [[ 1 ]u y = [10][* x2] The performance index is given by: J = (x[1 001 ]x + u?) dt J } " ]+ 0 Determine the LQR gain matrix analytical and by using Matlab software and then implement the LQR controller system using Matlab/Simulink and finally, compare the results obtained from Matlab script and Simulink model