1. A flow control system is described by the following differential equation. a. set of first order y(t)+5y(t)+6y(t) = u(t) Determine the state space model (controllable canonical form) of the continuous system, using x₁(t)= y(t), x(t) = y(t) x(t) = Ax(t) + bu(t) y(t) = cx(t) [5 marks] b. Obtain the transfer function of the continuous time model. [5 marks] C. d Solve for the transition matrix of the continuous time system, D(t). [5 marks] Evaluate the equivalent discrete time state space model matrices, D(kl) and I(k), if the input signal is sampled-hold with a sampling period, T= 0.1 second. [5 marks]