The authors study the feedback stabilization of linear systems given by a pair of matrices (F,G) with entries in a commutative normed

$\mathbb{K}$- algebra

${B}_{0}$ with identity. The problem is to find a suitable feedback matrix L over

${B}_{0}$ such that the closed loop system is stable. The system is transformed into another system

$(\widehat{F},\widehat{G})$ over a commutative

${C}^{*}$-algebra, where

$\widehat{\phantom{\rule{4pt}{0ex}}}$ means the Gelfand transform. Necessary and sufficient conditions for the stabilizability of

$(\widehat{F},\widehat{G})$ are obtained in terms of the corresponding Riccati equation. If the image

${\widehat{B}}_{0}$ or

$\widehat{B}$(B: the completion of

${B}_{0})$ under the Gelfand transform is *-closed, it is shown that the stabilizability of (F,G) is equivalent to that of

$(\widehat{F},\widehat{G})$. Another condition for the stabilizability of (F,G) is stated in terms of local stabilizability of the system which is equivalent to the local rank condition for

$(\widehat{F},\widehat{G})$. An example is shown as to the positioning of a seismic cable which is written by a discrete-time linear equation.