y(3) +11y +38y(1) + 404 = u(3) + 18u(2) + 954(1) + 126u = where y(2)(0) = 0, y(1)(0) = 0.5, y(0) 1, and u(2)(0) = u(1)(0) = u(0) 0. Note that y(n) means the nth-order derivative of y and u(n) means the nth-order derivative of u. Note also that the initial conditions are not zero. (i) Obtain the state space equation of the ODE system (Note that the initial conditions are not zero). Specify the definition of the state. Specify the elements of the state vector. Specify the initial condition of the state vector. G(s) = G(s) + G2(s) where Gi(s) = 1. Then it is not easy to obtain the state equations of G1 and G2. Then add them to obtain the state equation of G. (ii) By hand, compute the eigenvalues and eigenvectors of the system matrix in (i) (iii) Obtain the solution of the state space equation in (i). You need to compute eAt and specify the initial condition of the state. (iv) Compute limt700 y(t). What do you think about the initial condition? Does the initial condition affect the value of limt7oo y(t). Why or why not? Justify your answer y(3) +11y +38y(1) + 404 = u(3) + 18u(2) + 954(1) + 126u = where y(2)(0) = 0, y(1)(0) = 0.5, y(0) 1, and u(2)(0) = u(1)(0) = u(0) 0. Note that y(n) means the nth-order derivative of y and u(n) means the nth-order derivative of u. Note also that the initial conditions are not zero. (i) Obtain the state space equation of the ODE system (Note that the initial conditions are not zero). Specify the definition of the state. Specify the elements of the state vector. Specify the initial condition of the state vector. G(s) = G(s) + G2(s) where Gi(s) = 1. Then it is not easy to obtain the state equations of G1 and G2. Then add them to obtain the state equation of G. (ii) By hand, compute the eigenvalues and eigenvectors of the system matrix in (i) (iii) Obtain the solution of the state space equation in (i). You need to compute eAt and specify the initial condition of the state. (iv) Compute limt700 y(t). What do you think about the initial condition? Does the initial condition affect the value of limt7oo y(t). Why or why not? Justify your