This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. Many solved examples are intended in this book, in addition to a variety of unsolved relied pro

Abstract

Robust controller design requires a proper definition of uncertainty bounds. These uncertainty bounds are commonly selected randomly and conservatively for certain stability, without regard for controller performance.  This issue becomes critically important for multivariable systems with high nonlinearities, as in Active Magnetic Bearings (AMB) System. Flexibility and advanced learning abilities of intelligent techniques make them appealing for uncertainty estimation. The aim of this paper is to describe the development of robust H₂/H_∞ controller for AMB based on intelligent estimation of uncertainty bounds using Adaptive Neuro Fuzzy Inference System (ANFIS).  Simulatio

Abstract 

This paper presents an intelligent model reference adaptive control (MRAC) utilizing a self-recurrent wavelet neural network (SRWNN) to control nonlinear systems. The proposed SRWNN is an improved version of a previously reported wavelet neural network (WNN). In particular, this improvement was achieved by adopting two modifications to the original WNN structure. These modifications include, firstly, the utilization of a specific initialization phase to improve the convergence to the optimal weight values, and secondly, the inclusion of self-feedback weights to the wavelons of the wavelet layer. Furthermore, an on-line training procedure was proposed to enhance the control per

The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S

A novel robust finite time disturbance observer (RFTDO) based on an independent output-finite time composite control (FTCC) scheme is proposed for an air conditioning-system temperature and humidity regulation. The variable air volume (VAV) of the system is represented by two first-order mathematical models for the temperature and humidity dynamics. In the temperature loop dynamics, a RFTDO temperature (RFTDO-T) and an FTCC temperature (FTCC-T) are designed to estimate and reject the lumped disturbances of the temperature subsystem. In the humidity loop, a robust output of the FTCC humidity (FTCC-H) and RFTDO humidity (RFTDO-H) are also designed to estimate and reject the lumped disturbances of the humidity subsystem. Based on Lyapunov theo

      The article examines the definition of the verb in the form of the imperative mood (imperative) _ general information about the verb in Russian .

       A verb in Russian is one of the parts of speech that unify all parts of speech, expressing the meaning of action, movement, process in grammatical forms of time, type, mood, face and voice. The imperative mood is a grammatical feature of the verb expressed through several forms of the verb that urges someone to do things. In other words, imperative mood or (imperative) : -  one of the single meaning of the form . The form of the imperative expresses a supplicatio

В статье рассматривается вопрос о связи флективных изменений с мыслительными процессами на материале русского и арабского языков, анализируются семантические, фонетические, морфологические и синтаксические основы фонограмматической когниции. Цель статьи выявление прямой связи между количественным звуковым изменением согласного состава слова и мыслительными процессами, с помощью которых человеческ

The work in this paper involves the planning, design and implementation of a mobile learning system called Nahrain Mobile Learning System (NMLS). This system provides complete teaching resources, which can be accessed by the students, instructors and administrators through the mobile phones. It presents a viable alternative to Electronic learning. It focuses on the mobility and flexibility of the learning practice, and emphasizes the interaction between the learner and learning content. System users are categorized into three categories: administrators, instructors and students. Different learning activities can be carried out throughout the system, offering necessary communication tools to allow the users to communicate with each other