• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.3
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• pp.457-462
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• 2016

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen's integral inequality was the best in the last two decades until Seuret's integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret's integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2489-2492
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• 2003

In this paper, observer-based H$\sub$$\infty$/ controller design method for singular systems with time-varying delay by Just one LMI condition is presented. The sufficient condition for the existence of controller and the controller design method are presented by one perfect LMI approach. The design procedure involves solving an LMI. Since the obtained condition can be expressed as an LMI form, all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement and changes of variables.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.401-404
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• 1998

In this paper, we present robust reliable $H\infty$ controller design methods of continuous and discrete uncertain time delay systems through LMI(linear matrix inequality) approach, respectively. Also the existence conditions of state feedback control are proposed. Using some changes of varables and Schur complements, the obtained sufficient conditions are transformed into LMI form. We show the validity of the proposed method through numerical examples.

• Proceedings of the KIEE Conference
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• 2004.05a
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• pp.7-9
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• 2004

This paper provides an observer-based $H_{\infty}$ controller design method for singular systems with and without time-varying delay by just one LMI condition. The sufficient condition for the existence of controller and the controller design method are presented by perfect LMI (linear matrix inequality) approach. The design procedure involves solving an LMI. The observer-based $H_{\infty}$ controller in the existing results can be constructed from the coupled two or more conditions while the proposed controller design method can be obtained from an LMI condition, which can be solved efficiently by convex optimization. Since the obtained condition can be expressed as an LMI form, all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement and changes of variables. An example is given to illustrate the results.

• Journal of Astronomy and Space Sciences
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• v.4 no.2
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• pp.69-80
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• 1987

A photometric solutions of T LMi were derived with the Wilson and Devinney model using the BV photoelectric light curves of Okazaki(1977) and orbital period changes are discussed from the all of the collected times a available in the literature. We obtained a variation with a period of $62.^y01$ and an amplitude of $0.^d0425$ form the (O-C) diagram. According to the physical properties of T LMi on the basis of derived photometric solution, it have a doubt the credibility of the existence of "R CMa type".ype".uot;.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.44.1-44
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• 2002

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 a 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 upper bound of guaranteed cost function can be obtained simultaneously.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.948-953
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• 2001

Nonlinear dynamic equation of a 4-axis rigid rotor supported by two an-isotropic magnetic bearings is derived via Hamilton's principle. It is transformed to a state-space form for the standard Η$_{\infty}$ control problem. we present a robust Η$_{\infty}$ control design methods of continuous and discrete LMI-based approaches and improve performance using loopshaping.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.121-127
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• 1999

In this paper, we present robust reliable H$\infty$ controller design methods of continuous and discrete uncertain time delay systems using LMI (linear matrix inequality) technique, respectively. Also the existence conditions of state feedback control are proposed . Using some changes of variables and Schur complements, the obtained sufficient conditions are transformed into an LMI form. The closed loop system by the obtained controller is quadratically stable with H$\infty$ norm bound for all admissible uncertainties, time delay, and all actuator failures occurred within the prespecified set. We show the validity of the proposed method through numerical example.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.3
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• pp.172-179
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• 2003

Linear matrix Inequality based $H_\infty$ robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard $H_\infty$ control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based $H_\infty$ control is revealed.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.6-11
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• 2014

Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.