Digital redesign of pseudo-continuous-time suboptimal regulators for large-scale discrete systems

A multi-stage pseudo-continuous-time state-space method is developed for designing large-scale discrete systems, which do not exhibit a two- or multi-time scale structure explicity. The pseudo-continuous-time regulator places the eigenvalues of the closed-loop discrete system near the common region of a circle and a logarithmic spiral in the complex z-plane, without explicitly utilizing the open-loop eigenvalues of the given system. The method requires the solutions of small order Riccati equations only at each stage of the design. Based on matching all the states at all the sampling instants, a new digital redesign technique is presented for finding the pseudo-continuous-time quadratic regulator. An illustrative example is presented.