Robust Static Output Feedback $\mathcal {H}_\infty$ Control for Uncertain Takagi–Sugeno Fuzzy Systems

Elias, Leandro J.; Faria, Flávio A.; Araujo, Rayza; Magossi, Rafael F. Q.; Oliveira, Vilma A.

doi:10.1109/tfuzz.2022.3152836

Cited by 18 publications

(9 citation statements)

References 41 publications

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“…Finally, by applying the Schur complement to (30) and (31), we obtain (11) and (12). In other words, if there exists a solution to the matrix inequalities of ( 11) and ( 12), then the following inequality is guaranteed:…”

Section: Controller Designmentioning

confidence: 99%

“…Thus, there has been active research on H ∞ control; for instance, in [30], H ∞ performance criteria were applied to handle exogenous inputs, and ref. [31] derived static output feedback design conditions for uncertain T-S fuzzy systems under H ∞ performance using switched control methods. Previous research used a fixed H ∞ performance index, leading to conservativeness issues.…”

Section: Introductionmentioning

confidence: 99%

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Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

An,

Kim

2024

Actuators

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This paper proposes a sampled-data fuzzy controller design technique for an autonomous underwater vehicle (AUV) depth system represented by an interval type-2 (IT-2) fuzzy model, considering input saturation. In the Takagi–Sugeno (T–S) fuzzy model of an AUV depth system, surge velocity is chosen as a premise variable. To address the associated uncertainty with this variable, we employ the IT-2 fuzzy modeling technique. Also, the controller proposed in this paper utilizes time-varying gains, ensuring superior exponential stability compared with traditional fixed gain approaches. Furthermore, a membership function-dependent (MFD) H∞ criterion is employed to enhance robustness for each subsystem individually. Taking into account the mentioned aspects, the controller design condition is derived in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is validated through simulation examples.

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Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

An,

Kim

2024

Actuators

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“…Up to now, a large number of scholars have studied T-SFSs and made some achievements. Also, numerous interesting control approaches have been developed, such as the dynamic event-triggered security control 17 , the networked fault detection control 18 , the robust static output feedback 𝐻 ∞ control 19 , the stability and stabilization control 20 . It is necessary to point out that in 18 -20 , the interaction between linear subsystems divided by IF-THEN rules is not considered.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Anti-disturbance Switching Control for Switched T-S Fuzzy Systems

Zhao

Gao

Sang

et al. 2023

Preprint

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In this paper, an adaptive anti-disturbance switching (AADS) control strategy is proposed for switched Takagi-Sugeno fuzzy systems (ST-SFSs) subject to multi-source disturbances. The disturbances consist of two parts: the available unmodeled disturbance and the disturbance modeled by dynamic neural network. Firstly, a novel adaptive disturbance observer is designed to approximate the dynamic neural network modeled disturbance. Secondly, the attenuation performance from the output to the available disturbance is analyzed by the L 2 gain index. Thirdly, a controller based on the adaptive disturbance observer is constructed for the ST-SFS under the average dwell time switching signal limitation. Further, under the designed adaptive disturbance observer, and the controller, a sufficient condition is established for the ST-SFS to realize multi-source disturbance suppression (DS). Finally, a mass-spring-damping simulation example is given to verify the rationality of the established AADS control scheme.

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“…In existing works, numerous technologies have been proposed to reduce the conservatism of SO stability criteria. In accordance with the structure of the T-S fuzzy model, the Lyapunov function with a parameter-dependent structure [12][13][14] was provided to reduce the conservatism of stability analysis. In that Lyapunov function, the number matrices representing the weighting of system energy is dependent on the number of fuzzy rules.…”

Section: Introductionmentioning

confidence: 99%

“…In that Lyapunov function, the number matrices representing the weighting of system energy is dependent on the number of fuzzy rules. Based on [13,14], the Lyapunov function in the parameter-dependent case provides a less conservative result than the regular case in analyzing the stability of T-S fuzzy models. However, a latent conservatism in the parameter-dependent Lyapunov function is brought by the derivative term in the membership function.…”

Section: Introductionmentioning

confidence: 99%

Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

Huang,

Sun,

et al. 2023

Mathematics

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This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise.

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Robust Static Output Feedback $\mathcal {H}_\infty$ Control for Uncertain Takagi–Sugeno Fuzzy Systems

Cited by 18 publications

References 41 publications

Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

Adaptive Anti-disturbance Switching Control for Switched T-S Fuzzy Systems

Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

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