5. The state-space representation for 2x + 4x' + 5x = 10e¹ is 0 0 = [₁]. + + [9] e 98 99 910 0 1 6. Calculate the eigenvalue of the state-space coefficient matrix [-₁ using the methods -7a -2a demonstrated in your lecture notes (Note that a is a positive constant, do not assume values for a). If your eigenvalues are real and different, let ₁ be the smaller of the two eigenvalues when comparing their absolute values, for example, if your eigenvalues are -3 and 7, their absolute values are 3 and 7 with 3 < 7 and ₁ = -3. If your eigenvalues are a complex conjugate pair, let ₁ be the eigenvalue with the positive imaginary part. The eigenvalue you must keep is 2₁ : = q11a + 912 a j Note that if is real valued that 912 = 0 7. The general solution of a non homogeneous state-space equation is given below. Use the initial conditions to determine the value of C₁. X [*] = C₁ ¹² [2¹₁] + €₁₂-²¹ [ 2 ] + [4] given Xx(0) = 0,x(0) = 2 C₁e(2j) t C₂e-2jt x' You calculated that C₁ = 913+914 j Note that if C₁ is a real number that 914 = 0. et
