A method of compensator design for discrete systems which bounds both the closed-loop system and compensator eigenvalues

A method for designing compensators for discrete systems is presented. This method gives upper bounds on the maximum eigenvalues of the compensator and closed loop system by simultaneously minimizing the maximum singular values of the system matrices of the controller (A-BF), observer (A-LC) and compensator (A-BF-LC+BGC) for a given realization (A,B,C). However, the fact that the maximum singular values are minimized for a given realization does not imply any specific bounds on these values since they depend on the realization. Thus, an attempt is made to find bounds on the resulting maximum singular values based on various realizations. For certain systems, it is shown that the closed loop system and the compensator have maximum eigenvalues less than or equal to those of the original system