17.2 (Repeated eigenvalues). Consider the SISO LTI system x/xAx+ Bu. y=Cx + Du, xЄR", u.ye R. (a) Assume that A is a diagonal matrix and B, C are column/row vectors with entries b; and ci, respectively. Write the controllability and observability matrices for this system. (b) Show that if A is a diagonal matrix with repeated eigenvalues, then the pair (A, B) cannot be controllable and the pair (A, C) cannot be observable. (c) Can you find a SISO minimal realization for which the matrix A is diagonalizable with repeated eigenvalues? Justify your answer. (d) Can you find a SISO minimal realization for which the matrix A is not diagonal- izable with repeated eigenvalues? Justify your answer. Hint: An example suffices to justify the answer "yes" in (c) or (d).