Exact eigenvalue placement for two-time-scale discrete-time systems

Linear shift-invariant discrete-time systems satisfying the two-time-scale property are considered. A transformation matrix is formed and applied to the system to separate its slow and fast modes. Two subsystems are then defined, one for the slow modes and the other for the fast modes. An eigenvalue placement technique is proposed that will place the eigenvalues of the closed loop sub-systems at desired locations. The composite controller will also be formed for the original system.