• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.5
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• pp.33-40
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• 1996

In this paper, we propose the discrete model reduction method of bounded real transfer functions. From the discrete bounded real lemma, we obtain the two riccati equations and define the disrete bounded real balancing using solutions of these two riccati equations. And we get the reduced order discrete model from the GSPA of full order model. Especially, when free parameter of GSPA is .+-.1, we show that the reduced order discrete model retains minimality, stability, and bounded real and BR-balancing properties. And we derive the .inf.-norm error bound between full order model and reduced order model. Finally to illustrate the validity of proposed method, we give an example.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.157-162
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• 1998

This paper provides some properties of positive real systems in time domain. It is well-known that a positive real system and a bounded real system are closely related by bilinear transform in a frequency domain. By using supply rate and storage function, we show that a positive real system can be transformed into a bounded real system, and that a positive real system can be transformed into another positive real system with in a time domain. Also, we show that an ESPR(extended strictly positive real) system can be decomposed into a feedback system of lossless positive real system and another ESPR system. These results may be used to design an output feedback controller for mixed H$H_2$ESPR problem.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.104.4-104
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• 2001

This paper addresses a supervisory control problem to meet bounded time constraints in real-time nondeterministic discrete event systems (DESs) represented as timed transition models. For a timed language specification representing a bounded time constraint, this paper introduces the notions of trace-controllability and time-controllability. Based on the notions, this paper presents the necessary and sufficient conditions for the existence of a supervisor for a real-time nondeterministic DES to achieve the specification.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.1
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• pp.1-10
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• 1999

We consider the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear tune-Invariant plant such that a given closed loop transfer function is strictly sector bounded. We show that the standard $H{\infty}$ control problem and the $\tau$ -positive real control problem are special cases of sector bounded control problem. Necessary and sufficient conditions for the existence of a controller are obtained. The state-space representation for strictly proper controllers are given in terms of solutions to ARIs or AREs.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.7-27
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• 2015

Kuneth formula is to compute (co)-homology of $A{\otimes}B$ for known (co)-homology of the complexes A and B. In the ordinary case, this is done by using elementary homological methods in an abelian category. However, when we consider the bounded cochain complex with values in $\mathbb{R}$ and its structure as a real Banach space, the techniques of homological algebra for constructing K$\ddot{u}$nneth type formulas on it are not effective. The most notable facts are the image of a morphism of Banach spaces is not necessarily closed, and also the closed summand of a Banach space need not be a topological direct summand. The main goal of this paper is to construct the theory of K$\ddot{u}$nneth type formula on bounded cohomology with real coefficients in the suitable category of Banach spaces with some restricted conditions.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-890
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• 2020

In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G)⨶B*(K) is isomorphic to the bounded cohomology Ĥ*(G × K) of G × K, which is the cohomology of B*(G × K) as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients ℝ. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ*(G × K) to the seminorm in the cohomology of B*(G)⨶B*(K).

• Honam Mathematical Journal
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• v.41 no.3
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• pp.631-650
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• 2019

In this paper, for discrete groups G and K, we show that the bounded cohomology group of $G{\times}K$ is isomorphic to the cohomology group of the complex of the projective tensor product $B^*(G){\hat{\otimes}}B^*(K)$, where $B^*(G)$ and $B^*(G)$ are the complexes of bounded cochains with real coefficients ${\mathbb{R}}$ of G and K, respectively.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.105-114
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• 2001

In this paper we introduce the concepts of generalized bounded variation with respect to a strictly increasing function and Denjoy-Stieltjes integral of real-valued functions and then prove some properties of them.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.1-19
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• 1986

We show that a (possibly unbounded) linear operator, T, is scalar on the real line (spectral operator of scalar type, with real spectrum) if and only if (iT) generates a uniformly bounded semigroup and $(1-iT)(1+iT)^{-1}$ is scalar on the unit circle. T is scalar on [0, $\infty$) if and only if T generates a uniformly bounded semigroup and $(1+T)^{-1}$ is scalar on [0,1). By analogy with these results, we define $C^0$-scalar, on the real line, or [0. $\infty$), for an unbounded operator. We show that a generator of a positive-definite group is $C^0$-scalar on the real line. and a generator of a completely monotone semigroup is $C^0$-scalar on [0, $\infty$). We give sufficient conditions for a closed operator, T, to generate a positive-definite group: the sequence < $\phi(T^{n}x)$ > $_{n=0}^{\infty}$ must equal the moments of a positive measure on the real line, for sufficiently many positive $\phi$ in $X^{*}$, x in X. If the measures are supported on [0, $\infty$), then T generates a completely monotone semigroup. On a reflexive Banach lattice, these conditions are also necessary, and are equivalent to T being scalar, with positive projection-valued measure. T generates a completely monotone semigroup if and only if T is positive and m-dispersive and generates a bounded holomorphic semigroup.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).