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

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.101-109
• /
• 2002

We extend two inequalities involving Hadamard Products of Positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods we different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y Wang et al in [Lin. Alg. Appl. 302-303: 163-172(1999)] .

• Communications for Statistical Applications and Methods
• /
• v.5 no.3
• /
• pp.581-589
• /
• 1998

An algorithm is proposed for the $L_1$-estimation with linear equality and inequality constraints in linear regression model. The algorithm employs a linear scaling transformation to obtain the optimal solution of linear programming type problem. And a special scheme is used to maintain the feasibility of the updated solution at each iteration. The convergence of the proposed algorithm is proved. In addition, the updating and orthogonal decomposition techniques are employed to improve the computational efficiency and numerical stability.

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

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.125-133
• /
• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.441-460
• /
• 2016

We introduce the notions of h-v-semi-slant submersions and almost h-v-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations, investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. We find a condition for such submersions to be totally geodesic. We also obtain an inequality of a h-v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and h-v-semi-slant angle. Finally, we give examples of such maps.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.791-797
• /
• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.173-187
• /
• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.41 no.4
• /
• pp.29-37
• /
• 2004

This paper provides a reliable H$_{\infty}$ state feedback controller design method for delayed singular systems with actuator failures occurred within the prescribed subset. The sufficient condition for the existence of a reliable H$_{\infty}$ controller and the controller design method are presented by linear matrix inequality(LMI), singular value decomposition, Schur complements, and changes of variables. The proposed controller guarantees not only asymptotic stability but also H$_{\infty}$ norm bound in spite of existence of actuator failures. Since the obtained sufficient condition can be expressed as an LMI fen all variables can be calculated simultaneously. Moreover, the controller design method can be extended to the problem of robust reliable H$_{\infty}$ controller design method for singular systems with parameter uncertainties, time-varying delay, and actuator failures. A numerical example is given to illustrate the validity of the result.

• Korean Journal of Social Welfare Studies
• /
• v.42 no.1
• /
• pp.333-370
• /
• 2011

This study views the aged inequalities according to the inequality hypothesis of the life course perspective in OECD 10 countries. Focusing on educational level which is early social status and welfare state regime which is social structure factors of inequality, this study analyzes income inequality for the aged who have transformed into old age period from non-aged period. The analysis is based on the data SHARE of Europe and HRS of USA. The main results of this study are summarized in four points. First, the income inequality is quite high by welfare system and the educational level. Second, the income inequality is somewhat reduced in case the people move from the period of non-aged to the period of aged. However, gini coefficient is still high(0.475). Considering welfare state regimes, although the income inequality is high in conservative regime of non-aged period, this would be higher in aged period. This result supports cumulative advantages/disadvantages hypothesis. The liberal regime remains high income inequality which supports the theoretical argument of status maintenance. Social democratic regime provides evidence to offer some support for the status leveling hypothesis. In there, income inequality is lower in aged period even though income inequality of non-aged period is low. Third, the cumulative advantages/disadvantages of disposable income according to educational level are strengthened and heterogeneity is grown in case people transition from the late period of non-aged to aged period. But public pension has been more equally distributed than gross income. Fourth, seeing welfare state regimes, public pension of aged-period is more inequally distributed than that of non-aged period in liberal and conservative regime. Specially in conservative regime, inequality of gross income is very high and public pension is also inequally distribute So this might show that the social security system strengthens the cumulative advantages/disadvantages. However, in the social democratic regime, public pension is more equally distributed than gross income and it could be much more equally distributed in aged period, which can support the status leveling hypothesis.