Stability analysis and controller synthesis for fuzzy descriptor systems

Huang, Chih-Peng

doi:10.1080/00207721.2011.577248

Cited by 31 publications

(10 citation statements)

References 28 publications

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“…Lemma 7 (see [44]). The nominal system( ) = ( ) is admissible if and only if there exist a positive definite matrix and a matrix with appropriate dimensions such that…”

Section: Admissible and -Admissible Analysismentioning

confidence: 99%

SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Huang

2016

Mathematical Problems in Engineering

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Stability analysis issues and controller synthesis for descriptor systems with parametric uncertainty in the derivative matrix are discussed in this paper. The proposed descriptor system can extend the system's modeling extent of physical and engineering systems from the traditional state-space model. First, based on the extended -stability definitions for the descriptor model, necessary and sufficient admissibility and -admissibility conditions for the unforced nominal descriptor system are derived and formulated by compact forms with strict linear matrix inequality (LMI) manner. In contrast, existing results need to involve nonstrict LMIs, which cannot be evaluated by current LMI solvers and need some extra treatments. Deducing from the obtained distinct results, the roust admissibility and -admissibility of the descriptor system with uncertainties in both the derivative matrix and the system's matrices thus can be coped. Furthermore, by involving a proportional and derivative state feedback (PDSF) control law, we further address the controller design for the resulting closed-loop systems. Since all the proposed criteria are explicitly expressed in terms of the strict LMIs, we can use applicable LMI solvers for evaluating the feasible solutions. Finally, the efficiency and practicability of the proposed approach are demonstrated by two illustrative examples.

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“…Lemma 7 (see [44]). The nominal system( ) = ( ) is admissible if and only if there exist a positive definite matrix and a matrix with appropriate dimensions such that…”

Section: Admissible and -Admissible Analysismentioning

confidence: 99%

SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Huang

2016

Mathematical Problems in Engineering

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“…Based on the above research results of the T-S LSD system, we can know that output feedback or state feedback is still the main control method of the T-S LSD system [28,29]. However, in order to effectively discuss the stability of the descriptor system, the PD feedback method is proposed [30,31]. When the descriptor system is transformed into a singular system, we need to ensure the singular system is impulse-free and regular.…”

Section: Introductionmentioning

confidence: 99%

Passive Decentralized Fuzzy Control for Takagi-Sugeno Fuzzy Model Based Large-Scale Descriptor Systems

Chang

2022

IEEE Access

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“…Afterwards, considering the system with time delay, the PDC controller design method of these systems is given without all the subsystems which are regular and impulse-free in [10]. In [11], PDC and proportional-derivative state feedback controller for fuzzy singular systems with different derivative matrices are designed. In [12], the dissipativity analysis and controller design for a class of fuzzy descriptor systems with different derivative matrices are studied.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

Qiao

2021

Complexity

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The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.

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Stability analysis and controller synthesis for fuzzy descriptor systems

Cited by 31 publications

References 28 publications

SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Passive Decentralized Fuzzy Control for Takagi-Sugeno Fuzzy Model Based Large-Scale Descriptor Systems

Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

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