Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
A stability approach to fuzzy control design for nonlinear systems
Fuzzy Sets and Systems
Application of limit fuzzy controllers to stability analysis
Fuzzy Sets and Systems
Study on stability of fuzzy closed-loop control systems
Fuzzy Sets and Systems
Adaptive fuzzy systems and control: design and stability analysis
Adaptive fuzzy systems and control: design and stability analysis
Analysis and design of fuzzy control systems using dynamic fuzzy global models
Fuzzy Sets and Systems
A course in fuzzy systems and control
A course in fuzzy systems and control
Robust stability analysis of fuzzy control systems
Fuzzy Sets and Systems
Fuzzy modeling and model-based control for nonlinear systems
Applications of fuzzy logic
Quadratic stability analysis of the Takagi-Sugeno fuzzy model
Fuzzy Sets and Systems
L2-stabilization design for fuzzy control systems
Fuzzy Sets and Systems
A modified Hausdorff distance between fuzzy sets
Information Sciences: an International Journal
Fuzzy Control and Fuzzy Systems
Fuzzy Control and Fuzzy Systems
Soft Computing and Its Applications
Soft Computing and Its Applications
Brief note on the variation of constants formula for fuzzy differential equations
Fuzzy Sets and Systems
Knowledge-Based Clustering: From Data to Information Granules
Knowledge-Based Clustering: From Data to Information Granules
Toward a generalized theory of uncertainty (GTU): an outline
Information Sciences—Informatics and Computer Science: An International Journal
Stability analysis of fuzzy control systems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Stable adaptive fuzzy controllers with application to inverted pendulum tracking
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Stability analysis of fuzzy large-scale systems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Designing stable MIMO fuzzy controllers
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
TSK fuzzy systems types II and III stability analysis: continuous case
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
On the stability of fuzzy systems
IEEE Transactions on Fuzzy Systems
Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control
IEEE Transactions on Fuzzy Systems
On the stability issues of linear Takagi-Sugeno fuzzy models
IEEE Transactions on Fuzzy Systems
Robust stability analysis and design method for the fuzzy feedback linearization regulator
IEEE Transactions on Fuzzy Systems
Stability and periodicity in fuzzy differential equations
IEEE Transactions on Fuzzy Systems
Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities
IEEE Transactions on Fuzzy Systems
Recurrent neuro-fuzzy networks for nonlinear process modeling
IEEE Transactions on Neural Networks
Fuzzy logic-based generalized decision theory with imperfect information
Information Sciences: an International Journal
Information Sciences: an International Journal
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Stability is one of the fundamental concepts of complex dynamical systems including physical, economical, socioeconomical, and technical systems. In classical terms, the notion of stability inherently associates with any dynamical system and determines whether a system under consideration reaches equilibrium after being exposed to disturbances. Predominantly, this concept comes with a binary (Boolean) quantification (viz., we either quantify that systems are stable or not stable). While in some cases, this definition is well justifiable, with the growing complexity and diversity of systems one could seriously question the Boolean nature of the definition and its underlying semantics. This becomes predominantly visible in human-oriented quantification of stability in which we commonly encounter statements quantifying stability through some linguistic terms such as, e.g., absolutely unstable, highly unstable,. . ., absolutely stable, and alike. To formulate human-oriented definitions of stability, we may resort ourselves to the use of a so-called Precisiated Natural Language, which comes as a subset of natural language and one of whose functions is redefining existing concepts, such as stability, optimality, and alike. Being prompted by the discrepancy of the definition of stability and the Boolean character of the concept itself, in this paper, we introduce and develop a Generalized Theory of Stability (GTS) for analysis of complex dynamical systems described by fuzzy differential equations. Different human-centric definitions of stability of dynamical systems are introduced. We also discuss and contrast several fundamental concepts of fuzzy stability, namely, fuzzy stability of systems, binary stability of fuzzy system, and binary stability of systems by showing that all of them arise as special cases of the proposed GTS. The introduced definitions offer an important ability to quantify the concept of stability using some continuous quantification (that is through the use of degrees of stability). In this manner, we radically depart from the previous binary character of the definition. We establish some criteria concerning generalized stability for a wide class of continuous dynamical systems. Next, we present a series of illustrative examples which demonstrate the essence of the concept, and at the same time, stress that the existing Boolean techniques are not capable of capturing the essence of linguistic stability. We also apply the obtained results to investigate the stability of an economical system and show its usefulness in the design of nonlinear fuzzy control systems given some predefined degree of stability.