This paper discusses using H2 and H∞ robust control approaches for designing control systems. These approaches are applied to elementary control system designs, and their respective implementation and pros and cons are introduced. The H∞ control synthesis mainly enforces closed-loop stability, covering some physical constraints and limitations. While noise rejection and disturbance attenuation are more naturally expressed in performance optimization, which can represent the H₂ control synthesis problem. The paper also applies these two methodologies to multi-plant systems to study the stability and performance of the designed controllers. Simulation results show that the H2 controller tracks a desirable cl

     Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

In this paper ,we introduce hollow modules with respect to an arbitrary submodule .Let M be a non-zero module and T be a submodule of M .We say that M is aT-hollow module if every proper submodule K of M such that T ⊈ K is a T-small submodule of M .We investigate the basic properties of a T-hollow module

The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

Abstract

Through this study, I tried to identify the grammatical efforts of one of the most important authors of the footnotes that were built on the luminous benefits marked with (Explanation of Mulla Jami in Grammar), and he is Sheikh Isamah Allah Al-Bukhari, who died in the eleventh century AH, trying as much as possible to stay away from the path of tradition in repeating the efforts of Those who preceded me in explaining the grammatical efforts of many grammarians, and perhaps what helped me in this is the characteristics that characterize the notes owners that may distinguish them from other owners of grammatical authorship, as a result of what characterized the personality of the notes owners from the predominance of the in

     In the present study, the properties of the light elements, namely, H, He, Li, and Be, have been reviewed. Specifically, the nuclear decay of these nuclei has been reviewed. The mystery of the nuclear decay and potential is behind this work. The role of neutron has been investigated. The N/Z ratio has also been investigated in the study to relate the nuclear decay with the ratio. A new formula for nuclear potential has been suggested in the present study. This formula can describe the binding energy potential and the decayed particle energy depending on the N/Z ratio.

     The purpose of this paper is to introduce dual notions of two known concepts which are semi-essential submodules and semi-uniform modules. We call these concepts; cosemi-essential submodules and cosemi-uniform modules respectively. Also, we verify that these concepts form generalizations of two well-known classes; coessential submodules and couniform modules respectively. Some conditions are considered to obtain the equivalence between cosemi-uniform and couniform. Furthermore, the relationships of cosemi-uniform module with other related concepts are studied, and some conditional characterizations of cosemi-uniform modules are investigated.

  Numerous integral and local electron density’s topological parameters of significant metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp* Ir) (Cp Ru)₂ (μ₃-H) (μ-H)₃]1 (Cp = η⁵ -C₅Me₅), (Cp* = η⁵ -C₅Me₄Et) were calculated and interpreted by using the quantum theory of atoms in molecules (QTAIM). The properties of bond critical points such as the delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇²ρ(r), the local energy density

The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every es