Answer Happy

For the system described by the block diagram shown in Figure Q4 below, do the following: a) Derive a set of state space equations for the system using the indicated state variables. [6 marks] b) Investigate the controllability and observability properties of the system as the parameter a varies. [9 marks] c) Assume the state space equations of Q4.a) are written in matrix form as dtdx​=Ax+bu and apply state feedback u=f⊤x. Find the state feedback gain fT=[f1​​f2​​] as function of the parameter a such that the closed-loop characteristic polynomial is ϕ(s)=s2+2s+5. [10 marks]