Kazumi Horiguchi

Minimal realizations interpolating first- and second-order information

In this paper, we consider the problem of finding minimal realizations of multivariable linear stable discrete-time systems which interpolate the given first- and second-order information. We present the condition for the existence of a solution to this interpolation problem, the discriminant of its uniqueness and a parametrization of the class of all the solutions. The results may be applied to the design of digital filters, model reduction preserving stability, and the ARMA modelling of multivariable systems.

Controller Reduction Considering 2nd-Order Information

We propose a method of controller reduction, which aims to replace an ideal high-order controller with a reduced-order one so that finite numbers of 1st-and 2nd-order information of the closed-loop system can be preserved. The preserved 1st-and 2nd-order information are those associated with the transfer characteristics of the closed-loop system and its power spectrum characteristics at appropriate complex frequency points, respectively. The proposed method provides the reduced-order controller which yields a frequency-weighted approximation of the closed-loop system considering its stability.

A minimal lattice realization for multivariable systems

Abstract An algorithm for constructing a minimal lattice realization of a multivariable stable linear discrete-time system is proposed. The algorithm consists of four steps: (i) realize the objective system in an input normal Hessenberg form, (ii) construct an LBR system associated with the objective system, (iii) construct a lattice realization of the LBR system from its input normal Hessenberg realization, (iv) transform the lattice realization of the LBR system into one of the objective system.