• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.356-362
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• 2002

In this paper, well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. Based on the fuzzy models, a numerical robust stability analysis for the fuzzy feedback linearization regulator is presented using Linear Matrix Inequalities (LMI) Theory. For these structured uncertainty, the closed system can be cast into Lur'e system by simple transformation. From the LMI stability condition for Lur'e system, we can derive the robust stability condition for the fuzzy feedback linearization regulator based on Takagi-Sugeno fuzzy model. The effectiveness of the proposed analysis is illustrated by a simple example.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.801-803
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• 1995

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptation controllers which guarrantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1324-1329
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• 2004

In this article we have tested stability of classifier based on fuzzy similarity in generalized Lukasiewicz structure. Two different tests for stability was made:In on test stability was checked respect to weight parameters and other test was carried out for idealvectors. Tests have made with three different classification problems.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.135-147
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• 2018

Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.397-407
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• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.91-106
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• 2012

In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.1-14
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• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.411-424
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• 2010

In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

• Journal of Electrical Engineering and information Science
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• v.2 no.4
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• pp.28-36
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• 1997

In this paper, robust stability analysis for the fuzzy feedback linearization regulator is presented. Well-known Takagi-Sugeno fuzzy model is used as the MISO nonlinear plant model. Uncertainty and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainty and disturbances, robust stability of the close system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed by using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. The proposed stability analysis is illustrated by a simple example.