An Efficient Computational Algorithm for Solving Arbitrary Sylvester Matrix Equations in Fuzzy Control Theory (S/O 14179)

• Main Authors: Ahmad, Nazihah, Ibrahim, Haslinda
• Format: Monograph
• Language: English
• Published: UUM 2021
• Subjects: QA Mathematics
• Online Access: https://repo.uum.edu.my/id/eprint/31516/1/14179.pdf; https://repo.uum.edu.my/id/eprint/31516/

Sylvester matrix equation plays a vital role in stability analysis and controller design in control theory and other branches of engineering. However, the classical Sylvester matrix equations are less adequate to deal with any uncertainty problems during the system process, such as conflicting requirements or distraction of any elements and noise. Therefore, in the case of uncertainty in the parameters of classical Sylvester matrix equations, there is a need to embed the fuzzy theory whereby the parameters are in the form of fuzzy numbers. To date, work on fully fuzzy Sylvester matrix equation (FFSME) involved some limitations that include the fuzzy arithmetic operations, the type of fuzzy coefficients and the singularity of Sylvester matrix coefficients. Therefore, this study establishes a computational algorithm for solving Sylvester matrix equations with all the coefficients of the matrix equations are arbitrary left-right triangular fuzzy numbers (LR-TFN), which either positive, negative or near-zero.In constructing the algorithm, some modifications on the existing fuzzy subtraction and multiplication arithmetic operators are necessary. By modifying the existing fuzzy arithmetic operators, the constructed algorithm exceeds the positive restriction to allow the negative and near-zero LR-TFN as the coefficients of the equations. The constructed algorithm also utilized the Kronecker product and Vec-operator in transforming the fully fuzzy Sylvester matrix equations to a simpler form of equations. On top of that, new associated linear systems are developed based on the modified fuzzy multiplication arithmetic operators. The constructed algorithm is verified by presenting some numerical examples of two types of FFSME and also complex FFSME. As a result, the constructed algorithm has successfully demonstrated the solutions for the arbitrary FFSME, with minimum complexity of the fuzzy operations. The constructed algorithm is applicable for singular and non-singular matrices regardless of the size of the matrix. With that, the constructed algorithm is considered as a new contribution to the application of control system theory