• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.50-55
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• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.477-486
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• 2001

In this paper , we study the problem of designing TS(Takagi-Sugeno) fuzzy controllers for the systems that can be approximated or represented by the TS fuzzy model. The main strategy used in this paper is the inverse optimal approach, in which the cost function is determined later than the Lyapunov function and its corresponding control input satisfying the design requirements such as stability, decay rate, and robustness against uncertainty. This approach is useful because it yields controllers satisfying the inherent robustness of optimal controllers as well as the considered design goals. The design procedures established in this paper are all in the from of solving LMIs(Iinear matrix inequalities). Since the LMIs arising in the design procedures can be solved within a given tolerance by the interior point methods. the design method of the paper are efficient in practice. The applicability of the proposed design procedures is demonstrated by design examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.6
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• pp.747-752
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• 2006

In this paper, the adaptive fuzzy sliding mode controller with two systems is designed. The existing sliding mode controller used to $approximation{\^{u}}(t)$ with discrete sgn function and sat function for keeping the state trajectories on the sliding surface[1]. The proposed controller decrease the disturbance for uncertain control gain and This paper is concerned with an Adaptive Fuzzy Sliding Mode Control(AFSMC) that the fuzzy systems ate used to approximate the unknown functions of nonlinear system. In the adaptive fuzzy system, we adopt the adaptive law to approximate the dynamics of the nonlinear plant and to adjust the parameters of AFSMC. The stability of the suggested control system is proved via Lyapunov stability theorem, and convergence and robustness properties ate demonstrated. Futhermore, fuzzy tuning improve tracking abilities by changing some sliding conditions. In the traditional sliding mode control, ${\eta}$ is a positive constant. The increase of ${\eta}$ has led to a significant decrease in the rise time. However, this has resulted in higher overshoot. Therefore the proposed ${\eta}$ tuning AFSMC improve the performances, so that the controller can track the trajectories faster and more exactly than ordinary controller. The simulation results demonstrate that the performance is improved and the system also exhibits stability.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1732-1733
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• 2011

This paper presents observer-based controller design for interval type-2 fuzzy system with staircase membership approximation. In type-2 fuzzy case, membership function is itself fuzzy set itself. Thus, type-2 fuzzy system can deal with parametric uncertainties of nonlinear system by capturing the uncertainties in membership function. Likewise, stabilization condition of type-2 fuzzy system is derived from quadratic Lyapunov function, and it goes to linear matrix inequality. Furthermore, in this paper, to relax the conservativeness of stabilization condition, staircase membership function approximating method is applied. Observer-based control method is adopted to control system which has some unmeasurable states. To prove suitability of our proposed method, numerical example is presented.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.4
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• pp.499-505
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• 2011

In this paper, we proposed an adaptive fuzzy sliding mode control for nonlinear systems without parameter projection method. By modifying the controller structure, the parameters of the estimated input gain function are guaranteed not being identically zero and it is shown that the control scheme will not cause any implementation problem even if the estimated value of input gain function is zero at any moment during on-line operations. Except for the input gain function which an approximate estimate for its lower bound is needed, the proposed control scheme does not assume a priori the exact values of the bounding parameters. Based on Lyapunov synthesis methods, the overall control system guarantees that the tracking error asymptotically converges to zero and that all signals involved in controller are uniformly bounded. This can be illustrated by the simulation results for an inverted pendulum system.