A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems

Lee, Dong Hwan; Park, Jin Bae; Joo, Young Hoon

doi:10.1109/tfuzz.2011.2142315

Cited by 103 publications

(29 citation statements)

References 22 publications

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“…In this section, sufficient stability conditions of the T-S fuzzy system (3) which were proposed in [8] is introduced . Also the NFLF is adopted, and two assumptions (9) are considered.…”

Section: Stability Analysismentioning

confidence: 99%

“…In [3], [4], membership functions are considered in the Lyapunov method. In [5], [6], non-parallel distributed compensation (NPDC), which is the fuzzy controller dose not share the same fuzzy sets with the fuzzy systems, is used, and in [7], [8], the Lyapunov functions are changed for presenting relaxed stability and stabilization conditions. Especially, changing Lyapunov functions is one of the main issues to reduce con- [10].…”

Section: Introductionmentioning

confidence: 99%

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Controller Design for Continuous-Time Takagi-Sugeno Fuzzy Systems with Fuzzy Lyapunov Functions : LMI Approach

Kim¹,

Joo²,

Park³

2012

International Journal of Fuzzy Logic and Intelligent Systems

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This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI Toolbox. Simulation examples are given to illustrate the effectiveness of this method.

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“…In this section, sufficient stability conditions of the T-S fuzzy system (3) which were proposed in [8] is introduced . Also the NFLF is adopted, and two assumptions (9) are considered.…”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controller Design for Continuous-Time Takagi-Sugeno Fuzzy Systems with Fuzzy Lyapunov Functions : LMI Approach

Kim¹,

Joo²,

Park³

2012

International Journal of Fuzzy Logic and Intelligent Systems

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“…Since a common Lyapunov matrix is used for all local models of fuzzy systems, the quadratic Lyapunov function approach often leads to conservative results. Then parameter dependent Lyapunov functions (or called fuzzy Lyapunov functions) [24], [11], [19], [17], [36], piecewise Lyapunov functions [13], [23] and k-sample variation Lyapunov functions [16] are respectively proposed for reducing the conservatism introduced by using quadratic Lyapunov functions. On the other hand, by sharing the same fuzzy rules with the fuzzy models, parallel distributed compensation (PDC) control schemes [29] are often used for designing fuzzy controllers in the existing literature.…”

Section: Introductionmentioning

confidence: 99%

“…,(22)} are determined by selecting [−2, −2] as the eigenvalues of the subsystems in the PDC controller(17). Figs.…”

mentioning

confidence: 99%

Stability Analysis of T–S Fuzzy Control Systems by Using Set Theory

Dong

Yang

Zhang

2015

IEEE Trans. Fuzzy Syst.

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This paper is concerned with the stability analysis for T-S fuzzy control systems. By exploiting the property of the structure of fuzzy inference engine, an equivalence relation on index set of the product of fuzzy rule weights is defined. Further, a new stability criterion is proposed by using the equivalence relation, and formulated into progressively less conservative sets of linear matrix inequalities. By using an extension of Pólya's Theorem, the new criterion is proved to be with no conservatism for quadratic stability analysis of T-S fuzzy control systems with a product inference engine and any possible fuzzy membership functions. A numerical example is given to illustrate the effectiveness of the proposed method.Index Terms-T-S fuzzy control systems, stability analysis, equivalence class, set theory, linear matrix inequalities (LMIs).

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“…However, it is recognized that the common quadratic Lyapunov function is independent of membership functions, which may lead to conservativeness. To further reduce the conservatism in stability analysis, several non-quadratic Lyapunov functions have been proposed, such as piecewise Lyapunov functions [4,5,22] and fuzzy Lyapunov functions [1,2,8,12,15,17,18].…”

Section: Introductionmentioning

confidence: 99%

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Zhao¹,

Xiao²,

Ding³

et al. 2014

Kybernetika

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A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems

Cited by 103 publications

References 22 publications

Controller Design for Continuous-Time Takagi-Sugeno Fuzzy Systems with Fuzzy Lyapunov Functions : LMI Approach

Controller Design for Continuous-Time Takagi-Sugeno Fuzzy Systems with Fuzzy Lyapunov Functions : LMI Approach

Stability Analysis of T–S Fuzzy Control Systems by Using Set Theory

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

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