AKSESIBILITAS SIKLIS DARI STATE-STATE TERCAPAI MENGKARAKTERISASI RING REGULER VON NEUMANN; CYCLIC ACCESSIBILITY OF REACHABLE STATES CHARACTERIZES VON NEUMANN REGULAR RINGS

JEROL VIDEL LIOW, Ari Suparwanto

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

Let R be a commutative ring with 1. Ring R has a feedback cyclization property if for any reachable system (A;B) over R, there is a matrix K and a vector u such that (A;B) and the single-input system (A + BK;Bu) have the same reachable submodule. In this paper, we introduced the generalization of the feedback cyclization property to non-necessarily reachable systems. We prove that if R is a von Neumann regular ring, then R has the generalized feedback cyclization property. On the other hand, the generalization of feedback cyclization property characterizes von Neumann regular rings. From the proof of the main theorem, we give an algorithm to find K and u, named cyclization algorithm, and an example.

Kata Kunci : CYCLIC ACCESSIBILITY, REACHABLE STATES, VON NEUMANN REGULAR RINGS