Consider the system described by the following difference equation y(k+1)=3 y(k-1)-2 y(k-2)+u(k)-2 u(k-1)+u(k-2) a) What is the transfer function? Is the system stable? Does the system have a stable inverse? b) Is it possible to realize the system such that it is observable but not controllable? If yes, write down the corresponding state-space equation. If no, justify your answer. c) Is it possible to realize the system such that it is controllable but no tobservable? If yes, write down the corresponding state-space equation.If no, justify your answer. d) Is it possible to realize the system such that it is both controllable and observable? If yes, write down the corresponding state-space equation.If no, justify your answer.

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