A new solution of pair matrix equations with arbitrary triangular fuzzy numbers

Abstract

Pair matrix equations have numerous applications in control system engineering, such as for stability analysisof linear control systems and also for reduction of nonlinear control system models. There are some situations in whichthe classical pair matrix equations are not well equipped to deal with the uncertainty problem during the process ofstability analysis and reduction in control system engineering. Thus, this study presents a new algorithm for solving fullyfuzzy pair matrix equations where the parameters of the equations are arbitrary triangular fuzzy numbers. The fuzzyKronecker product and fuzzy V ec-operator are employed to transform the fully fuzzy pair matrix equations to a fullyfuzzy pair linear system. Then a new associated linear system is developed to convert the fully fuzzy pair linear systemto a crisp linear system. Finally, the solution is obtained by using a pseudoinverse method. Some related theoreticaldevelopments and examples are constructed to illustrate the proposed algorithm. The developed algorithm is also ableto solve the fuzzy pair matrix equation.