النشر العلمي

  • Response Analysis of Multiple-Input Multiple- Output Frequency and Singular Value Decomposition

Abstract

 

       Recently, developments in linear control theory have concentrated on the multiple-input multiple-output control systems (MIMO). Many systems, particularly in technologically advanced areas such as aerospace systems, are represented by models with several inputs, with each input having several outputs. Such cross-coupling makes the use of single-input, single-output (SISO) methods complicated. In this paper, we introduced the basic closed-loop expressions for MIMO. We then discussed 2-norms stability, and uncertainty. The standard design problem defined and solutions worked out.                                        

published in International Journal of Science and Research (IJSR) Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296 Volume 7 Issue 5, May 2018 ISSN (Online): 2319-7064

  • The Correspondence between Composite Functions in Modern Algebra and Calculus.

Abstract

 

   The study of maps which act on a finite set of objects is of especial importance in modern algebra. The main objective of this paper is to compare between the structures of groups that yield from the definition of composite functions in group theory (permutation groups) and those in calculus.

   In calculus there no detailed study for groups, but we took the definition of composite functions as a binary operation to define a group. This study can be considered as an essential model for isomorphic groups. 

published in Journal of Mathematical Theory and Modeling, IISTE ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol. 8. No. 3. 2018

  • THE LIENARD TYPE OF DEGREE FIVE WITH TWO LIMIT CYCLES

Abstract

 

     In this article, we study the limit cycles problem for Linard type of degree five, and we proved that the system has exactly two limit cycles under certain conditions. Also, we compared our result with method of calculating the amplitude of limit cycles by perturbation as in [4].      

 

published in Egypt. J. of Appl. Sci. 33 (5) May 2018 231-238

  • Partial-Fraction Expansion with MATLAB and Solving Linear, Time - Invariant, Differential Equations Using Laplace Transforms

Abstract

      In this paper we are concerned with MATLAB program to find the expansion of the partial-fraction for complicated functions with denominator involving higher-order polynomials, instead of using the inverse of Laplace transform for partial-fraction expansion, which is to solve the linear, time-invariant, differential equations. In the results discussion, four examples are used to demonstrate the solution of linear, time-invariant, differential equations by the Laplace transform method and MATLAB program to find the partial-fraction expansion.             

 

published in Egypt. J. of Appl. Sci. 29 (7) July 2014 90-102

  • Accuracy and Stability for Closed Loop (Feedback) Control System

  Abstract

        An advantage of the closed-loop control system is the fact that the use of feedback makes the system response relatively insensitive to external disturbances and internal variations in system parameters. In this paper we studied how Accuracy and stability of closed loop systems can be determined by investigating how signals propagate around the feedback loop.

    The criterion represented off-shoot of the Hurwitz determinants idea, but made the computations much simpler through which is known as a Routh table. The Nyquist stability theorem is a key result that provides a way to analyze stability and introduced measures of degrees of stability.

published in Sudan J. for Basic Sci., M (SJBS) Series (Math.) No. 13, 2018

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