(40 points) Consider a discrete-time system Ck+1 = AXk, X(0) = X0 where A E Rnxn is a real constant matrix. Then, the following state- ments are equivalent. i) All the eigenvalues of A are located on the open unit disc; :00+ > - 11921 3 'ud " oxA (! k=0 iii) 3P = PT and Q = QT > 0 s.t. ATPA - P = -Q; iv) Vxo ER", lim Ck = 0