We consider the following problem: For a system consisting of two submodules, the behavior of one submodule is known as well as the desired behavior S of the global system. What should be the behavior of the second submodule such that the behavior of the composition of the two submodules conforms to S ?-This problem has also been called "equation solving", and in the context of supervisory cont...

A method for solving CCS equations of type (AIX)\L ~ B, where X is unknown, is presented. The method is useful in a top-down design methodology: if a system (B) and some of its submodules (.4) axe specified, solving such an equation amounts to constructing the missing submodules. The method works by successively transforming equations into simpler equations, in parallel with generation of a sol...

The full-bridge submodule (FBSM)-based modular multilevel converter (FBSM-MMC) offers promising performance due to its ability output negative FBSM voltage. This paper studies this of the FBSM-MMC under zero-sequence voltage injection (ZSVI) and second-order harmonic current (SHCI). focus research is redistribute powers by injecting an additional power degree freedom, resulting in a smaller cap...

As an abstraction of the geometric notion of translation, author in [8] has introduced two operators T+ and Tcalled the fuzzy translation operators on the fuzzy set and studied their properties and also investigated the action of these operators on the (Anti) fuzzy subgroups of a group in [8] and (Anti) fuzzy subring and ideal of a ring in [9]. The notion of anti fuzzy submodule of a module h...

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $...

Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.