• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.6
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• pp.46-54
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• 1998

This paper presents a method for designing robust fuzzy $H^{\infty}$ controllers which stabilize nonlinear systems with parameter uncertainty adn guarantee an induced $L_{2}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Takagi and Sugeno's fuzzy models with uncertainty are used as the model for the uncertain nonlinear systems. Fuzzy control systems utilize the concept of so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the stability condition satisfying decay rate and disturbance attenuation condition for Takagi and Sugeno's fuzzy model with parameter uncertainty are discussed. A sufficient condition for the existence of robust fuzzy $H^{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMIs). Finally, design examples of robust fuzzy $H^{\infty}$ controllers for uncertain nonlinear systems are presented.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1037-1041
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• 2004

This paper examines the problem of designing an $H_{\infty}$ fuzzy state-feedback controller for a class of uncertain nonlinear descriptor systems which is described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an $H_{\infty}$ state-feedback controller which guarantees the $L_2$-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of systems. A numerical example is provided to illustrate the design developed in this paper.

• Journal of the Korean Society for Precision Engineering
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• v.31 no.2
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• pp.105-112
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• 2014

This paper proposes a novel $H{\infty}$ T-S Fuzzy controller with a weighted integral action for Interior Permanent Magnet Synchronous Motor(IPMSM) which have nonlinear dynamics. The $H{\infty}$ T-S Fuzzy controller is used for the robustness of nonlinear systems and the weighted integral action is used for the tracking problem and the improvement of control performance. A T-S Fuzzy controller is designed by combining the local controllers with the overall stability, and LMI(Linear Matrix Inequality)is used to determine the gains of linear controllers. The tracking problem of IPMSM is changed into regulator problem by introducing the integral action and the weighting factor gives flexibility to a $H{\infty}$ fuzzy controller.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.840-847
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• 2009

This paper deals with an $H_{\infty}$ output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the $H_{\infty}$ norm of the uncertain singularly perturbed fuzzy system is less than $\gamma$ for a sufficiently small $\varepsilon$ > 0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than $\gamma$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter $\varepsilon$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.379-381
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• 2004

In this paper, a robust $H_{\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H_{\infty}$ controllers are given in terms of linear matrix inequalities.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.149-152
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• 2005

In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.429-434
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• 2016

This paper introduces a stabilization condition for polynomial fuzzy systems that guarantees $H_{\infty}$ performance under the imperfect premise matching. An $H_{\infty}$ control of polynomial fuzzy systems attenuates the effect of external disturbance. Under the imperfect premise matching, a polynomial fuzzy model and controller do not share the same membership functions. Therefore, a polynomial fuzzy controller has an enhanced design flexibility and inherent robustness to handle parameter uncertainties. In this paper, the stabilization conditions are derived from the polynomial Lyapunov function and numerically solved by the sum-of-squares (SOS) method. A simulation example and comparison of the performance are provided to verify the stability analysis results and demonstrate the effectiveness of the proposed stabilization conditions.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.28-35
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• 2012

This paper presents the method for $H_{\infty}$ fuzzy controller design of discrete-time fuzzy Markovian jump systems with state and input time delays. The Takagi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the fuzzy Markovian jump systems with state and input time delays. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller is given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficiency of the proposed design method.

• International Journal of Control, Automation, and Systems
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• v.5 no.3
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• pp.349-354
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• 2007

This paper considers the problem of designing static output feedback controllers for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. Based on linear matrix inequality technique, a new method is developed for designing fuzzy stabilizing controllers via static output feedback. Furthermore, the result is also extended to $H_{\infty}$ control. Examples are given to illustrate the effectiveness of the proposed methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.11
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• pp.1620-1627
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• 2017

In this paper, we design an observer-based $H_{\infty}$ fuzzy controller for interval type-2 Takagi-Sugeno (T-S) fuzzy systems under imperfect premise matching. The designed observer-based controller can effectively estimate the state of the system and make fuzzy system satisfy the $H_{\infty}$ disturbance attenuation performance. Using the slack matrix, the derived stabilization condition is expressed in terms of a linear matrix inequality. Finally, the effectiveness of the proposed method is verified through a simulation example.