• Journal of the Korean Mathematical Society
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• 제34권2호
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• pp.469-481
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• 1997

In this paper we consider TU-cooperative games in the form of characteristic function. We notice that if one uses the necessary and sufficient condition for the core to be not empty in a dual form, it may be used for selecting the final outcome in the core. Using the linear programming approach for constructing the subcore, which is a subset of the core, we represent it in a simple form. We consider reduced games due to Davis-Mashler, Moulin and Funaki and formulate the sufficient conditions for the subcore to be S-consistent.

• Bulletin of the Korean Mathematical Society
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• 제54권4호
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• pp.1173-1183
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• 2017

We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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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.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.323-330
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• 2014

The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

• Journal of the Korean Institute of Telematics and Electronics
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• 제25권2호
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• pp.162-167
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• 1988

In this note, we present some sufficient conditions on the structure of modelling uncertainties for output regualtion of uncertain systems. It turns out that these conditions include as special cases the ordinary matching conditions for stage regulation of uncertain systems and the disturbance decoupling condition. the previous restrictions on the structure of modelling uncertainties can be considerably relaxed in the case of output regulation. The significance of out result is illuminated through a simple example.

• Journal of the Chungcheong Mathematical Society
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• 제33권1호
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• Journal of the Korean Mathematical Society
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• 제46권5호
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• pp.1087-1103
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• 2009

Given a system of s independent 1-forms on a smooth manifold M of dimension m, we study the existence of integral manifolds by means of various generalized versions of the Frobenius theorem. In particular, we present necessary and sufficient conditions for there to exist s'-parameter (s' < s) family of integral manifolds of dimension p := m-s, and a necessary and sufficient condition for there to exist integral manifolds of dimension p', p' $\leq$ p. We also present examples and applications to complex analysis in several variables.

• Transactions on Control, Automation and Systems Engineering
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• 제2권1호
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• pp.19-23
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• 2000

In this paper, we deal with the problem of designing guaranteed cost state feedback controller for the generalized time-varying delay systems with delayed state and control input. The generalized time delay system problems solved on the basis of LMI(linear matrix inequality) technique considering time-varying delays. The sufficient condition for the existence of controller and guaranteed cost state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be reformulated as LMI forms in terms of transformed variables. Therefore, all solutions of LMIs, guaranteed cost controller gain, and guaranteed cost are obtained at the same time. The proposed controller design method can be extended into the problem of robust guaranteed cost controller design method for parameter uncertain systems with time-varying delays easily.

• Transactions on Control, Automation and Systems Engineering
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• 제4권3호
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• pp.199-204
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• 2002

This paper is concerned with H$_{\infty}$ controller design methods for descriptor systems with and without time-varying delays in state and control input. The sufficient condition for the existence of an H$_{\infty}$ controller and the controller design method are presented by linear matrix inequality (LMI), singular value decomposition, Schur complements, and changes of variables. Since the obtained sufficient condition can be changed to an LMI form by proper manipulations, all solutions including controller gain can be obtained at the same time. Moreover, it is shown that robust H$_{\infty}$ controller design problem for parameter uncertain descriptor systems with time-varying delays in state and control input can be solvable using the proposed method.

• Bulletin of the Korean Mathematical Society
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• 제22권2호
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• pp.95-98
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• 1985

In [1], E.B. Lee and L. Markus described a sufficient condition for which the domain of null-controllability of a linear autonomous system is all of R$^{n}$ . The purpose of this note is to extend the result to a certain linear nonautonomous system. Thus we consider a linear control system dx/dt = A(t)x+B(t)u in the Eculidean n-space R$^{n}$ where A(t) and B(t) are n*n and n*m matrices, respectively, which are continuous on 0.leq.t<.inf. and A(t) is a periodic matrix of period .omega.. Admissible controls are bounded measurable functions defined on some finite subintervals of [0, .inf.) having values in a certain convex set .ohm. in R$^{m}$ with the origin in its interior. And we present a sufficient condition for which the domain of null-controllability is all of R$^{n}$ .