u(s) Given the following block diagram a. (5 pts) Identify all loop gains. b. (5 pts) For the loops identified in (a), identify which are touching and non-touching. c. (5 pts) Identify all forward path gains. d. (5 pts) Using Mason's gain formula applied to the results of parts (a), (b) and (c), determine the transfer function G(s)=y(s)/u(s). e. (5 pts) Derive the state-space equations for the system in terms of the indicated state variables x and x. Clearly indicate the values for the matrices A, B, C and D. + 1 K + 1 X1 a K Ko 0 K3 1x S b + + y(s)