• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.6
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• pp.762-767
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• 2008

This paper introduces a $L_{\infty}$-gain state feedback fuzzy controller design for the time delay nonlinear system represented by Takagi-Sugeno(T-S) fuzzy model. First, the T-S fuzzy model is employed to represent the time delay nonlinear system. Next based on the fuzzy model, a fuzzy state feedback controller is developed to achieve $L_{\infty}$-gain performance. Finally, sufficient conditions are derived for $L_{\infty}$-gain performance. The sufficient conditions are formulated in the format of linear matrix inequalities (LMIs). The effectiveness of the proposed controller design methonology is finally demonstrated through numerical simulations.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.393-398
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• 1996

In this paper, we consider H.inf. control of nonlinear systems which have not only additive uncertainties but also input-multiplicative uncertainties. Using the relation between the L$_{2}$ gain of a nonlinear system and the Hamilton-Jacobi-Isaacs inequality, we define

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.111-114
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• 2003

In this paper, we consider the stabilization and $H_\infty$ control of linear systems with static output feedback control. The static output feedback control represents the simplest closed-loop control that can be realized in practice, and, moreover, it is less expensive to be implemented and is more reliable. In spite of its advantages, it is one of the open problems which is not sloved analytically or numerically yet. After decompose the closed-loop system into feedback form, by adopting the small gain theorem, we obtain a sufficient condition for stabilization and a sufficient condition for It control expressed as linear matrix inequalites. Finally, we show the usefulness of our results by a numerical example.

• Proceedings of the KIEE Conference
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• 1996.07b
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.412-415
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• 1995

Previously obtained results of L$_{2}$-gain and H$_{\infty}$ control via state feedback of nonlinear systems are extended to a class of nonlinear system with uncertainties. The required information about the uncertainties is that the uncertainties are bounded in Euclidian norm by known functions of the system state. The conditions are characterized in terms of the corresponding Hamilton-Jacobi equations or inequalities (HJEI). An algorithm for finding an approximate local solution of Hamilton-Jacobi equation is given. This results and algorithm are illustrated on a numerical example..

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.9
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• pp.1648-1654
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• 2007

In this paper, we consider the design of $H_\infty$ high-gain state feedback control for time-delayed linear systems with limited actuator capacities. The high-gain control means that the control permits the predetermined degree of saturation. Based on new Lyapunov-Krasovskii functional, we derive a result in the form of matrix inequalities. The matrix inequalities are consisted of LMIs those confirm the positive definiteness of Lyapunov- Krasovskii functional, satisfaction of predetermined degree of saturation, reachable set and $L_2$ gain constraint. The result is dependent on the bound of time-delay and its rate, predetermined degree of saturation, actuator capacity, and the allowed size of disturbances. Finally, we give a numerical example to show the effectiveness and usefulness of our result.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2040-2042
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• 2002

In this paper, we consider the design of gam scheduled controllers for linear systems with input saturation. We obtain a reachable set and a control gain, which guarantees that the controls are never saturated inside this reachable set and that the $L_2$ gain is minimized, from matrix inequalities. This proposed gain scheduled control gives better performance than that of static control case, and we present the simulation results to show the usefulness of the proposed control.

• 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.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.99-105
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• 1999

This paper presents a fuzzy H$\infty$ filtering problem for a class of uncertain nonlinear systems with time-varying delayed states and unknown inital state on the basis of Takagi-Sugeno(T-S) fuzzy model. The nonlinear systems are represented by T-S fuzzy models, and the fuzzy control systems utilize the concept of the so-called parallel distributed compensation. Using a single quadraic Lyapunov function, the stability and L2 gain performance from the noise signals to the estimation error are discussed. Sufficient conditions for the existence of fuzzy H$\infty$ filters are given in terms of linear matrix inequalities (LMIs). The filtering gains can also be directly obtained from the solutions of LMIs.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.9
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• pp.520-525
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• 2000

This paper deals with the design of H$\infty$ control for uncertain linear systems with the regional eigenvalue assignment constraint. The considered region is a disk in the left half plane and the two types of time-varying uncertainties are considered. We presents a state feedback control that minimize the L2 gain from the disturbance to the measured output as well as it guarantees that all eigenvalues of closed loop are inside a disk. The state feedback control is obtained by checking the feasibility of linear matrix inequalities (LMI's) which are numerically tractable. Finally we give an example to show the applicability and usefulness of our results.