• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.23-29
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• 1985

Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.$_{l}$ (.phi.(T)).contnd..sigma.$_{l}$ (T) for any operator T.mem.L(H) (Corollary 10), 3) For every operator T.mem.L(H), .sigma.$_{ap}$ (.phi.(T))=.sigma.$_{ap}$ (T))=.sigma.$_{ap}$ (T)=.sigma.$_{p}$(.phi.(T)) (Lemma 12, 13) and .sigma.$_{c}$(.phi.(T))=.sigma.(Theorem 15).15).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1689-1696
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• 2000

This paper proposes a new adaptive control scheme for flexible-link robots. A model-based nonlinear control scheme is designed based on a V-shape Lyapunov function, and then the nonlinear control i s extended to a model-based adaptive control to cope with parametric uncertainties in the dynamic model. The proposed control guarantees the global exponential or global asymptotic stability of the overall control system with all internal signals bounded. The effectiveness of the proposed control is shown by computer simulation.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1991.10a
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• pp.107-110
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• 1991

When the noise has both additive and signal-dependent components, locally optimum detector test statistics are obtained for detection of weak composite signals using the generalized Neyman-Pearson lemma. In order to consider the non-additive noise as well as purely-additive noise, a generalized observation model is used in this paper. The locally optimum detector test statistics are derived for several different cases according to the relative strengths of the known signal component, the random signal component, and the signal-dependent noise component. Schematic diagrams of the locally optimum detector structures are also included.

• The Mathematical Education
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• v.14 no.1
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• pp.22-26
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• 1975

In this paper, we define a differential module and study its properties. In section 2, as for propositions, Ive research some properties, directsum, isomorphism of factorization, exact sequence of derived modules. And then as for theorem, I try to present the following statement, if the sequence of homomorphisms of differential modules is exact. Then the sequence of homomorphisms of Z(X) is exact, also the sequence of homomorphisms of Z(X) is exact. According to the theorem, as for Lemma, we consider commutative diagram between exact sequence of Z(X) and exact sequence of Z'(X) . As an immediate consequence of this theorem, we obtain the following result. If M is an arbitrary module and the sequence of homomorphisms of the modules Z(X) is exact, then the sequence of their tensor products with the trivial endomorphism is semi-exact.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.361-372
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• 2006

This study was extended as one of the properties of isosceles triangles to polygons(n-angles) by conjectures-proofs-reputations-reformations and developed teaching-learning materials which can be used in high-level classes for middle and high school students.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.133-136
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• 1987

This paper presents a new algorithm of optimal measurement system by using band matrix characteristic respectively for state estimation. A performance index of measurement system is established to reflect relation among measurement sets, probability of measurement failure and cost of individual meter installation. Selection ranking in the candidates of measurement sets is composed to guarantee the observability for any any single meter outage. Performance index sensitivity is introduced and recursive formula which based on the matrix inversion lemma used for selection. The proposed algorithm is composed of successive addition algorithm, successive elimination algorithm and combinatorial algorithm. The band matrix characteristic could save in memory requirements and calculate the performance index faster than earlier.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.122-124
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• 1987

This paper presents a new algorithm in formulating a performance index for contingency selection method considering voltage security. Security limits defined-in terms of real power line flows and voltage magnitudes are considered in normalized subspaces where in critical contingencies are identified by a filtering algorithm using the infinite norm. Two types of limits, warning limit and emergency limit, are introduced for voltage and line flow. Usually performance indices have been constructed for real power line flows and voltages with each different criterion. This paper, however, presents a method that constructs them with the same criterion in use of the norm properties, so that we can assess security considering both of them. Rapid contingency simulation is performed using one iteration of fast decoupled load flows with LMML(Inverse Matrix Modification Lemma).

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.515-525
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• 2008

In this paper, the problem of delay-dependent stabilization for singular systems with multiple internal and external incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily test with numerical or algebraic methods. Based on Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memoryless state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free, and asymptotically stable via solving a strict linear matrix inequality (LMI) problem. An explicit expression for the desired memoryless state feedback control laws is also given. Finally, a numerical example illustrates the effectiveness and the availability for the proposed method.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.263-268
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• 2008

An improved linear matrix inequality (LMI) representation of delay-independent $H_2$ performance analysis is introduced for linear delay systems with delays of any size. Based on this representation we propose a new $H_2$ memoryless state feedback design. By introducing a new matrix variable, the new LMI formulation enables us to parameterize memoryles s controllers without involving the Lyapunov variables in the formulations. By using a parameter-dependent Lyapunov function, this new representation proposed here provides us the results with less conservatism.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.2
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• pp.121-127
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• 2009

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.