Discrete Hmodel matching problem by dynamic state feedback

Abstract

The model matching problem is one of the most familiar problems in the control theory. Let $T_m(z)$ and T(z) be stable and proper transfer matrices. The discrete $H_infty$ model matching problem is to find a controller transfer matrix R(z) which is stable and causal, to minimize the $H_infty$ norm of $T_m(z)$-T(z)R(z). The interpretation is this: $T_m(z)$ and T(z) are given as the model and the given system transfer matrices, respectively. Thus, the closed-loop performance T(z)R(z) approximates the desired performance Tm(z). In this paper, we consider the discrete $H_infty$ model matching problem with dynamic state feedback in the sense of $H_infty$ optimality criterion by using linear matrix inequalities approach. The main contribution could briefly be explained as to reformulate the discrete $H_infty$ model matching problem as a special discrete Ha optimal control problem in the formulation of linear matrix inequality, to derive a solvability condition for this special case and to give a design procedure for the controller of the discrete $H_infty$ model matching problem. It may be noted that the linear matrix inequality based parameterization of the controller provides the best performance of the discrete $H_infty$ model matching problem in the sense of $H_infty$, and the controller can be determined through the solution of only one linear matrix inequality.

Özet

Bu çalışmada bir ön kontrolörün eşdeğeri olan dinamik durum geribeslemesi ile ayrık $H_infty$, model eşleme probleminin doğrusal matris eşitsizlikleri yaklaşımı ile çözümü amaçlanmıştır. Ayrık $H_infty$ model eşleme problemi, ayrık $H_infty$ optimal kontrol probleminin özel bir halidir. Bu nedenle ayrık $H_infty$ optimal kontrol probleminin doğrusal matris eşitsizlikleri ile elde edilen çözümü ayrık $H_infty$, model eşleme probleminin çözülmesi için kullanılabilir. Makalede ayrık $H_infty$ model eşleme probleminin dinamik durum geribeslemesi ile çözümünün tek doğrusal matris eşitsizliğine indirgenebildiği gösterilmiş ve kontrolör tasarımı için gereken sentez teoremi ve algoritma verilmiştir.