• 제어로봇시스템학회논문지
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• 제7권3호
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• pp.183-192
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• 2001

In this paper, the decoupling H(sub)$\infty$ controller which minimizes the maximum energy in the output signal is designed to reduce the coupling properties between the input/output variables which make it difficult to control a system efficiently. The state-space formulas corresponding to the existing transfer matrix formulas of the controller are derived for computational efficiency. And for a given decoupling $H_{\infty}$ problem, an efficient method are sought to find the controller coefficients through the LMI(Linear Matrix Inequalities) method by which the problem is formulated into a convex optimization problem.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.100-104
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• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• International Journal of Control, Automation, and Systems
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• 제6권2호
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• pp.171-179
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• 2008

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.1131-1133
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• 1996

In this paper, we consider the mixed $L_1/H_{\infty}$ problems of finding internally stabilizing controllers which minimize the peak-to-peak gain of a certain closed loop transfer function with $H_{\infty}$-norm constraint on other closed loop transfer function(or vise versa). This problem is a useful framework for designing a controller with the norm constraints upon time and frequency domain. We formulate the mixed $L_1/H_{\infty}$ problem as LMI problems by using the reachable set. This paper offers the sufficient condition for the existence of suboptimal state feedback controller, and shows that suboptimal solution can be obtained by solving a finite-dimensional convex optimization and a line search.

• 대한기계학회논문집A
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• 제27권8호
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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.

• 한국지능시스템학회논문지
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• 제12권4호
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• pp.300-305
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• 2002

본 논문에서는 타원형 클러스터링을 위한 거리측정 함수로써 변형된 가우시안 커널 함수를 사용하며, 주어진 클러스터링 문제를 각 타원형 클러스터의 체적을 최소화하는 문 로 해석하고 이를 선형행렬 부등식 기법 중 하나인 고유값 문제로 변환하여 최적화하는 새로운 알고리즘을 제안한다.

• 전자공학회논문지SC
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• 제39권5호
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• pp.18-25
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• 2002

본 논문에서는 컴퓨터 연산을 통한 언어형 퍼지 제어 시스템의 안정도를 해석하는 새로운 방법을 제안한다. 제안하는 방법은 최근 각광을 받고 있는 선형행렬부등식을 이용한 방법이다. 기존의 수치적 방법과 비교할 때 본 논문에서 제안되는 방식의 특징은 좀더 완화된 방식으로 안정화 문제뿐 아니라 고정점 레귤레이션 문제에도 적용될 수 있는 특징을 가지고 있다. 끝으로 컴퓨터 모의 실험을 통하여 제안한 방법의 타당성을 확인한다.

• 전기학회논문지
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• 제57권8호
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• pp.1429-1433
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• 2008

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

• 대한기계학회논문집A
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• 제30권10호
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1758-1763
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• 2004

This paper focuses on congestion control for ATM network with uncertain time-variant delays. The time-variant delays can be distinguished into two distinct components. The first one is represented by time-variant queueing delays in the intermediate switches that are occurred in the return paths of RM cells. The next one is a forward path delay. It is solved by the VBR model which quantifies the data propagation from the sources to the switch. Robust $H_8$ control is studied for solving congestion problem with norm-bounded time-varying uncertain parameters. The suitable robust $H_8$ controller is obtained from the solution of a convex optimization problem through LMI technique.