• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.7A
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• pp.967-977
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• 2000

In this paper, we apply a mixed $H_2/H_{\infty}$ control to a generalized plant of inverted pendulum system represented by an LFR(Linear Fractional Representation). First, in order to obtain the generalized plant, the linear model of the inverted pendulum represented by an LFR(Linear fractional Representation) is derived. In LFR, we consider system uncertainties as three nonlinear components and a pendulum mass uncertainty. Augmenting the LFR model by adding weighting functions, we get a generalized plant. And then, we design a mixed $H_2/H_{\infty}$ controller for the generalized plant. In order to design the mixed $H_2/H_{\infty}$ controller, we use the LMI technique. To evaluate control performances and robust stability of the mixed $H_2/H_{\infty}$ controller designed, we compare it with the $H_{\infty}$ controller through the simulation and experiment. In the result, with the fewer feedback information, the mixed $H_2/H_{\infty}$ controller shows the better control performances and robust stability than the $H_{\infty}$ controller in the sense of pendulum angle.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.5
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• pp.1111-1116
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• 2000

The mixed $H_2/ H_\infty$ control method is one of positive approaches to design a controller having both the$H_2$-performance and the $H_\infty$-robust stability. In this paper, Firstly, The tracking Performance to be designed has been represented as $H_2$-norms for the plants with uncertainties. Secondly, $H_\infty$-norm have been set up in order to ensure the robust stabilities. The mixed digital controllers have been designed for an inverted system. The mixed $H_2/ H_\infty$digital controller for the inverted pendulum system was intended to stabilize the unstability of the plant together with the good tracking Performance.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.239-245
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• 2002

In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.2
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• pp.316-321
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• 2007

[ $H{\infty}$ ] controller, which shows robustness for disturbances and noises, can not be used in the case of uncertain system parameters. Even if the $H{\infty}$ controller can be designed for the parameter uncertain system, its performance can be deteriorated. Therefore, in this paper, the robustness of $H{\infty}$ controller is improved by using the SMC(Sliding Mode Control). The LMI based $H{\infty}$ controller is designed first and then SMC controller is added.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.888-891
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• 1996

The objective of a mixed H$_{2}$/H$_{\infty}$ controller of active suspension system is to achieve not only the general performance improvement(H$_{2}$) but also the worst case disturbance rejection(H$_{\infty}$). In this paper, a mixed H$_{2}$/H$_{\infty}$ controller for an active suspension system, comparing the performance with that of an H$_{2}$ controller and of an H$_{\infty}$ controller.ler.EX> controller.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.2
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• pp.276-281
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• 2008

This paper proposes a new sliding surface which can have the same dynamics of nominal system based on SVM(Support Vector Machines). The conventional sliding mode control can not have the properties of $H_{\infty}$ controller because its sliding surface has lower order dynamics than the original system. The additional states must be used to solve this problem. However, The sliding surface of this paper can have the dynamics of $H_{\infty}$ control system by using support vector machines without defining any additional dynamic state. By using SVM, the property of $H_{\infty}$ control system can be estimated as a relationship between the states. With this relationship, a new sliding surface can be designed and have $H_{\infty}$ control system properties. As a result, in spite of the parameter uncertainty, the proposed controller can have the same dynamic of nominal system controlled by $H_{\infty}$ controller.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.37 no.5
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• pp.103-110
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• 2000

In This paper, we propose a design procedure for a SD $H_{\infty}$controller with PID performance. In developing the procedure, we use the basic idea of standard$H_{\infty}$problem, and then applied it to the SD system, which consists of the continuous plant and the discrete controller. This $H_{\infty}$controller design procedure involves the selections of weighting functions. The selections considered the relation of the closed loop specification between the $H_{\infty}$controller and PID. We illustrate this procedure in the controller design for a two-mass spring system.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.42 no.6
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• pp.9-14
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• 2005

In this paper, we consider the synthesis of non-fragile $H_{\infty}$ state feedback controllers for singular systems and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile $H_{\infty}$ controller, and the measure of non-fragility in controller are presented via LMI(linear matrix inequality) technique. Also, the sufficient condition can be rewritten as LMI form in terms of transformed variables through singular value decomposition, some changes of variables, and Schur complements. Therefore, the obtained non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop singular systems within a prescribed degree. Moreover, the controller design method can be extended to the problem of robust and non-fragile $H_{\infty}$ controller design method for singular systems with parameter uncertainties. Finally, a numerical example is given to illustrate the design method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2980-2988
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• 2000

In this paper, H(sub)$\infty$ depth and course controllers of autonomous underwater vehicles using H(sub)$\infty$ servo control are proposed. An H(sub)$\infty$ servo problem is foumulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the H(sub)$\infty$servo problem is as follows; firest, this problem is modified as an H(sub)$\infty$ control problem for the generalized plant that includes a reference input mode, and than a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach, The H(sub)$\infty$depth and course controllers are designed to satisfy the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under disturbances(was force, wave moment, tide). The performances(the robustness to the uncertainties, depth and course tracking properties) of the designed controlled are evaluated with computer simulations, and finally these simulation results show the usefulness and applicability of the propose H(sub)$\infty$ depth and course control systems.

• Journal of the Korea Institute of Military Science and Technology
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• v.3 no.1
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• pp.38-46
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• 2000

In this paper, robust depth and course controllers of AUV(autonomous underwater vehicles) using LMI-based H$_{\infty}$ servo control are proposed. The $H_{\infty}$ servo problem is modified to an $H_{\infty}$ control problem for the generalized plant that includes a reference input mode, and then a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach. The robust depth and course controllers are designed to be satisfied the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under sea wave and tide disturbances. The performances of the designed controllers are evaluated by computer simulations, and these simulation results show the applicability of the proposed robust depth and course controller.