How do I approach this?

Consider the ODE 2705) + 26W) + W) = 0 with the initial condition y(0) = 1; y(0) = 0. The problem is to find the value of 5 that minimizes \"I? = [O 92036515 a) Using :1: = [y y]: obtain a statespace representation of the form :tzAx, y=C$ Identify the matrices A and C. b) Write and solve a suitable Lyapunov equation to evaluate 77. Find the value of 6 that minimizes n. 0) Does the solution of the Lyapunov equation (for minimum 6) give a Lyapunov function? Why