• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.5
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• pp.8-17
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• 2002

This paper considers the problems of robust decentralized control for uncertain discrete-time large-scale systems with delays in interconnections and state feedback gain perturbations. Based on the Lyapunov method, the state feedback control design for robust stability is given in terms of solutions to a linear matrix inequality (LMI), and the measure of non-fragility in controller is presented. The solutions of the LMI can be easily obtained using efficient convex optimization techniques. A numerical example is included to illustrate the design procedures.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.300-305
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• 2002

In this paper, we use the modified gaussian kernel function as clustering distance measure and recast the given hyper-ellipsoidal clustering problem as the optimization problem that minimizes the volume of hyper-ellipsoidal clusters, respectively and solve this using EVP (eigen value problem) that is one of the LMI (linear matrix inequality) techniques.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.6
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• pp.7-14
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• 2000

This paper describes the synthesis of robust decentralized controllers for uncertain large-scale discrete-time systems with time-delays in subsystem interconnections. Based on the Lyapunov method, a sufficient condition for robust stability, is derived in terms of a linear matrix inequality (LMI). The solutions of the LMI can be easily obtained using various efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.3
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• pp.99-108
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• 2003

This paper is concerned with the problem of designing a guaranteed cost state feedback controller for singular systems with time-varying delays. The sufficient condition for the existence of guaranteed cost controller, the controller design method, and the optimization problem to get the upper bound of guaranteed cost function are proposed by LMI(linear matrix inequality), singular value decomposition, Schur complements, and change of variables. Since the obtained sufficient conditions can be changed to LMI form, all solutions including controller gain and the upper bound of guaranteed cost function can be obtained simultaneously. Moreover, the proposed controller design method can be extended to the problem of robust guaranteed cost controller design method for singular systems with parameter uncertainties and time-varying delays. The validity of the proposed design algorithm is investigated through a numerical example.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.582-589
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• 2003

This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included Un the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. $L_2$ robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1353-1362
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• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.10
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• pp.181-186
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• 2012

In this paper, we describe the synthesis of robust and non-fragile Kalman filter design for a class of uncertain linear system with polytopic uncertainties and filter gain variations. The sufficient condition of filter existence, the design method of robust non-fragile filter, and the measure of non-fragility in filter are presented via LMIs(Linear Matrix Inequality) technique. And the obtained sufficient condition can be represented as PLMIs(parameterized linear matrix inequalities) that is, coefficients of LMIs are functions of a parameter confined to a compact set. Since PLMIs generate infinite LMIs, we use relaxation technique, find the finite solution for robust non-fragile filter, and show that the resulting filter guarantees the asymptotic stability with parameter uncertainties and filter fragility. Finally, a numerical example will be shown.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1249-1254
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• 2006

Existing adaptive observers may cause the parameter drifts due to disturbances even if state estimation errors remain small. To avoid the drift phenomena in the presence of bounded disturbances, several robust adaptive observers have been introduced addressing bounds in state and parameter estimates. However, it is not easy for these observers to manipulate the size of the bounds with the selection of the observer gain. In order to reduce estimation errors, this paper introduces the (equation omitted) gain minimization problem in the adaptive observer structure, which minimizes the (equation omitted) gain between disturbances and estimation errors. The stability condition of the adaptive observer is reformulated as a linear matrix inequality, and the observer gain is optimally chosen by solving the convex optimization problem. The estimation performance is demonstrated through a numerical example.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.6
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• pp.38-45
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• 2001

In this paper, numerical stability analysis methodology for the singleton-type linguistic fuzzy control systems is proposed. The proposed stability analysis is not the analytical method but the numerical method using the convex optimization of Quadratic Programming (QP) and Linear Matrix Inequalities (LMI). Finally, the applicability of the suggested methodology is highlighted via simulation results.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.7
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• pp.56-64
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• 1999

In this paper, a novel approach to the stability analysis of the continuous affine Takagi-Sugeno fuzzy control systems is proposed. The suggested analysis method is easily implemented by the recently spotlighted convex optimization techniques called Linear Matrix Inequalities (LMI). First, it derives the stability condition under which the affine Takagi-Sugeno fuzzy system is stable in the large. Next, the derived condition is recast in the formulation of LMI and numerically addressed. Finally, the applicability of the suggested methodology is highlighted via computer simulations.