• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.3
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• pp.85-94
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• 2000

In this paper, a robust H$\infty$ optimal tuning problem of a structure-specified PSS is investigated for power systems with parameter variation and disturbance uncertainties. Genetic algorithm is employed for optimization method of PSS parameters. The objective function of the optimization problem is the H$\infty$-norm of a closed loop system. The constraint of the optimization problem are based on the stability of the controller, limits on the values of the parameters and the desired damping of the dominant oscillation mode. It is shown that the proposed H$\infty$ PSS tuned using genetic algorithm is more robust than conventional PSS.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.34-39
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• 1991

In this paper, we provide a treatment of the $H^{\infty}$-mixed sensitivity optimization approach to feedback system design. With compromising between the effect of a disturbance at the plant output and the effect of plant perturbations, we propose an algorithm to design robust controller. A $H^{\infty}$-optimization problem is to be equivalent to a Hankel-approximation, this enables the problem to be solved using state-space methods based on balanced realizations.s.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.516-523
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• 2006

This paper is concerned with the $H_{\infty}$ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified $H_{\infty}$ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for $H_{\infty}$ state feedback controllers is given by solving a certain LMI. The design problem of optimal $H_{\infty}$ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.750-753
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• 1998

This paper gives a simple parameterization of all stable unbiased filters to solve the suboptimal mixed $H_2/H_{\infty}$ filtering problem. Using the central filter, mixed $H_2/H_{\infty}$ filter is designed which minimizes the upper bound for the $H_2$ norm of the transfer matrix from a white noise to the estimation error subject to an $H_{\infty}$ norm constraint on the transfer matrix from an energy-bounded noise to the estimation error. The problem of finding suitable estimator gain can be converted into a convex optimization problem involving linear matrix inequalities.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.729-731
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• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.12
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• pp.655-660
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• 2004

This paper deals with the design of a fixed-structure $H_\infty$ power system stabilizer (PSS) by using an iterative linear matrix inequality (LMI) method. The fixed-structure $H_\infty$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the practical applicability of the proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.7
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• pp.615-623
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• 2008

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.46-51
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• 1991

An algorithm of finding a solution to an $H^{\infty}$-minimization problem is proposed, and the solution is obtained explicity in terms of closed-form. We construct an optimal controller subject to the interpolation constraints such that $H^{\infty}$-norm and the minimized value of transfer function matrix are equal.l.