This paper deals with the stability issues of fuzzy control systems in the framework of T-S fuzzy models and the parallel distributed compensation. A hyperellipsoid-based approach is proposed for the stability analysis and synthesis of T-S fuzzy models. The minimal hyperellipoids are constructed by employing the support information in the fuzzy rules. Then, the stability conditions for open-loo...

In formal language theory, we are mainly interested in the natural language computational aspects of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, we introduce two subclasses of fuzzy regular ω-languages called fuzzy n-local ω-languages and Buchi fuzzy n-local ω-languages, and give some closure properties for those subclasses. We define a ...

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧-fuzzy (implicative) ideal are provided. Some...

The concept of strongly α-continuous mappings by Y. Beceren [2] has been extended in topological spaces. We introduce and study fuzzy strongly αcontinuous maps on fuzzy topological spaces. Some of its properties have also been investigated. Relation between fuzzy strongly α-continuous and fuzzy αcontinuous map has also been established. The stronger form of fuzzy αcontinuous map is strongly α-c...

This paper presents the relaxed nonquadratic stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, we propose a new fuzzy controller and Lyapunov function by generalizing the nonparallel distributed compensation (non-PDC) control law and nonquadratic Lyapunov function, respectively. By exploiting Pólya’s theorem and algebraic properties of a homogeneous polyno...

This paper proposes a passive fuzzy controller design for the discrete ship steering system that is represented by the Takagi-Sugeno (T-S) fuzzy model with multiplicative noises. Applying the Lyapunov theory for guaranteeing mean square stability, the sufficient conditions are developed to design the fuzzy controller for the T-S fuzzy model with multiplicative noises. The sufficient conditions ...

This paper presents the stability conditions of the Takagi-Sugeno (T-S) fuzzy sampled-data filter. The error system between the T-S fuzzy system and fuzzy filter is presented. In the sense of the Lyapunov stability analysis, the stability conditions are given, which can be represented in terms of linear matrix inequalities (LMIs). The proposed stability conditions utilize the different approach...

We deal with an optimal control problem of the Bolza type, where the controlled system is governed by a generalized sweeping process, which is a special differential inclusion with discontinuous right-hand side. Employing a suitable constraint qualification, we restate the problem using distance functions and use the fuzzy sum rule to obtain fuzzy optimality conditions. Furthermore, we derive p...

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several...

According to fuzzy arithmetic, general dual fuzzy linear system (GDFLS) cannot be replaced by a fuzzy linear system (FLS). In this paper, we use new notation of fuzzy numbers and convert a GDFLS to two linear systems in crisp case, then we discuss complexity of the proposed method. Conditions for the existence of a unique fuzzy solution to n× n GDFLS are derived. AMS Subject Classification: 34K...