This paper presents a sum of squares (SOS) approach to guaranteed cost control of polynomial discrete fuzzy systems. First, we present a polynomial discrete fuzzy model that is more general representation of the well-known discrete Takagi-Sugeno (T-S) fuzzy model. Secondly, we derive a design condition based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special...

The paper investigates delay-dependent control and stability analysis for T−S fuzzy systems with a sensor delay. Based on a Lyapunov-Krasovskii function (LKF), a less conservative delay-dependent stability condition in the form of parameterized linear matrix inequalities (PLMIs) is established. In the derivation process, Jensen inequality is introduced to estimate the upper bound of the derivat...

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we prop...

Contrapositive symmetry (CPS) is a tautology in classical logic. In fuzzy logic, not all fuzzy implications have CPS with respect to a given strong negation. Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler and Kohout [Semantics of implication...

This paper demonstrates twometa-mathematical propositions concerning the increasingly popular “intuitionistic” (= vague) approaches to fuzzy sets and fuzzy topology, as well as the closely related interval-valued (= grey) sets and interval-valued “intuitionistic” sets: (1) the term “intuitionistic” in these contexts is historically inappropriate given the standard mathematical usage of “intuiti...

General topology can be regarded as a special case of fuzzy topology where all membership functions in question take values 0 and 1 only. The usual fuzzy metric spaces, fuzzy Hausdorff topological vector spaces, and Menger probabilistic metric spaces are all the special cases of F-type fuzzy topological spaces. Therefore, one would expect weaker results in the case of fuzzy topology. Recently s...

We introduce a new notion of fuzzy r -interior which is an extension of Chang’s fuzzy interior. Using fuzzy r -interior, we define fuzzy r -semiopen sets and fuzzy r semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang’s fuzzy topology, respectively. Some basic properties of fuzzy r -semiopen sets and fuzzy r -semicontinuous maps are invest...

The fuzzy H∞ filter design problem for T-S fuzzy systems with interval time-varying delay is investigated. The delay is considered as the time-varying delay being either differentiable uniformly bounded with delay derivative in bounded interval or fast varying with no restrictions on the delay derivative . A novel Lyapunov-Krasovskii functional is employed and a tighter upper bound of its deriv...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...