• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.10
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• pp.1854-1860
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• 2008

In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

• Journal of Electrical Engineering and Technology
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• v.8 no.5
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• pp.1202-1211
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• 2013

This paper deals with a robust controller for an induction motor (IM) which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback are associated. This approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic LPV system because of speed and rotor resistance affine dependence. Their values can be estimated on line during systems operations. The simulation and experimental results largely confirm the effectiveness of the proposed control.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.4
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• pp.617-621
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• 2012

This paper considers the synchronization problem of chaotic systems. For this problem, the sampled-data control approach is used to achieve asymptotic synchronization of two identical chaotic systems. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find the sampled-data feedback controller which achieves the synchronization between chaotic systems. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.5
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• pp.673-678
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• 2013

This paper considers the stability of linear systems having an interval time-varying delay using a switched system approach. The time-delay system is converted to the switched system equivalently, and then a stability criterion in the form of linear matrix inequality(LMI) is derived by using a parameter dependent Lyapunov-Krosovskii function(PD-LKF). In constructing a PD-LKF, the decomposition is employed for delay free intervals, and the reduction of conservatism is shown analytically as the number of decomposition increases. Finally, two well-known numerical examples are given to show the reduction of conservatism compared to the recent results.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.11
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• pp.741-746
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• 2004

When investigating a control problem for network based control systems, the main issue is network-induced delay. This delay can degrade the performance of control systems designed without considering the delay and even destabilize the system. In this paper, we consider the stabilization of network based control systems, where there is bounded time-varying delay. This delay is treated like parameter variation of a discrete time system. The state feedback controller design is formulated as linear matrix inequality. Finally, we show that the stability of control systems designed with considering the delay is superior to that is not so.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.494-496
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for uncertain linear systems with saturating actuators. We consider a general saturating actuator and employ the additive decomposition to deal with it effectively. And the considered uncertainty is the unstructured uncertainty which is only known its norm bound. Based on Linear Matrix Inequality(LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2564-2566
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• 2005

This paper presents an iterative linear matrix inequality (LMI) method for $H_2$ and $H_{\infty}$ optimal static output feedback (SOF) control, which is expressed in terms of LMIs subject to an additional rank condition. We propose a linear Penalty function to penalize the rank constraint so that static $H_2$ and $H_{\infty}$ synthesis results in solving a series of convex LMI optimization problems. Numerical experiments for various $H_2$ and $H_{\infty}$ SOF synthesis were performed to demonstrate the effectiveness of the proposed algorithm.

• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.226-228
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• 2005

This paper deals with power system stabilization problem using a network control system in which the control is applied through a communication channel in feedback form. Analysis and synthesis issues are investigated by modeling the packet delivery characteristics of the network as a Bernoulli random variable, which is described by a two state Markov chain. This model assumption yields an overall system which is described by a discrete-time Markov jump linear system. These employ the norm to measure the performance of the system, and they compute the norm via a necessary and sufficient matrix inequality condition.