Discrete linear quadratic regulators with eigenvalue placement in specified regions

A new procedure is presented for the design of discrete linear quadratic regulators in the frequency domain with eigenvalue placement at exact locations and/or within specified regions of the complex z-plane. The method utilizes the frequency domain optimality conditions for achieving the desired pole placement. Also, the proposed procedure is sequential and enables the retention of some stable open-loop eigenvalues and associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.