Admissibility Analysis and Control Synthesis for T-S Fuzzy Descriptor Systems

The problem of admissibility analysis and control synthesis for Takagi-Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor s...

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Published inIEEE transactions on fuzzy systems Vol. 25; no. 4; pp. 729 - 740
Main Authors Qiao, Liang, Zhang, Qingling, Zhang, Guofeng
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Admissible control
Compensation
Controllers
Design methodology
Fuzzy systems
Linear matrix inequalities
linear matrix inequalities (LMIs)
Lyapunov methods
Mathematical analysis
Mathematical models
Matrix methods
nonparallel distributed compensation (non-PDC) controller
nonquadratic fuzzy Lyapunov function
parallel distributed compensation (PDC) controller
PD control
Stability analysis
Symmetric matrices
Synthesis
Takagi–Sugeno (T–S) fuzzy descriptor system
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Abstract The problem of admissibility analysis and control synthesis for Takagi-Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.
AbstractList The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.
Author Qingling Zhang
Liang Qiao
Guofeng Zhang
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Snippet The problem of admissibility analysis and control synthesis for Takagi-Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy...
The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy...
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SubjectTerms Admissible control
Compensation
Controllers
Design methodology
Fuzzy systems
Linear matrix inequalities
linear matrix inequalities (LMIs)
Lyapunov methods
Mathematical analysis
Mathematical models
Matrix methods
nonparallel distributed compensation (non-PDC) controller
nonquadratic fuzzy Lyapunov function
parallel distributed compensation (PDC) controller
PD control
Stability analysis
Symmetric matrices
Synthesis
Takagi–Sugeno (T–S) fuzzy descriptor system
Title Admissibility Analysis and Control Synthesis for T-S Fuzzy Descriptor Systems
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