Stability Analysis for Interval Type-2 Fuzzy Systems by Applying Homogenous Polynomially Membership Functions Dependent Matrices and Switching Technique
Likui Wang, Hamid Reza Karimi, Junhua Gu
Abstract
In this article, the homogenous polynomially membership functions dependent (HPMFD) matrices are used to study the interval type-2 Takagi-Sugeno fuzzy systems. First, some necessary notations of the HPMFD matrices are introduced. Next, based on these notations, the time derivative of the HPMFD matrices is discussed and a switching method is proposed to ensure that the time derivative of the HPMFD matrices is negative. Then, a HPMFD controller is designed and new stabilization conditions are obtained by using the HPMFD Lyapunov function. In the end, the simulations show that the method in this article is less conservative than the existing ones in the literatures.
Topics & Concepts
Interval (graph theory)MathematicsController (irrigation)Fuzzy control systemFuzzy setDerivative (finance)Type (biology)Lyapunov functionFuzzy logicStability (learning theory)Control theory (sociology)Membership functionNotationTime derivativeApplied mathematicsComputer scienceControl (management)Nonlinear systemMathematical analysisCombinatoricsArithmeticArtificial intelligenceBiologyEconomicsQuantum mechanicsFinancial economicsPhysicsAgronomyEcologyMachine learningFuzzy Logic and Control SystemsAdvanced Data Processing TechniquesNeural Networks and Applications