• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.23-23
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• 2000

In this paper, we proposed the problems of robust stability and 개bust H$_{\infty}$ control of discrete time-delay linear st.stems with Frobenius norm-bounded uncertainties. The existence condition and the design method of robust H$_{\infty}$ state feedback control]or are given. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• 충청수학회지
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• 제19권3호
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• pp.237-244
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• 2006

In this paper, we examine the existence and bounded- ness of the solutions of discrete Volterra equations $$x(n)=f(n)+\sum_{j=0}^{n}g(n,j,x(j))$$, $n{\geq}0$ and $$x(n)=f(n)+\sum_{j=0}^{n}B(n,j)x(j)$$, $n{\geq}0$.

• 대한수학회논문집
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• 제37권3호
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• pp.705-718
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• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.

• 대한수학회논문집
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• 제37권1호
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• pp.91-103
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• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.

• 대한수학회지
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• 제48권6호
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• pp.1125-1142
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• 2011

In this paper, we define some new sequence spaces of infinite matrices regarded as operators on $l_2$ by using algebraic properties of such the matrices under the Schur product multiplication. Some of their basic properties as well as duality and preduality are discussed.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.455-458
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• 2003

An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method to find the matrix is shown. Simulations arc made for a weight-lifting operation of a two-link manipulator and the robust control performance of robotic systems by the proposed algorithm is remarkable.

• 한국정밀공학회지
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• 제20권12호
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• pp.176-182
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• 2003

An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method to find the matrix is shown. Simulations are made for a weight-lifting operation of a two-link manipulator and the robust control performance of robotic systems by the proposed algorithm is remarkable.

• International Journal of Control, Automation, and Systems
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• 제3권2호
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• pp.143-151
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• 2005

This paper considers a robust decentralized $H_\infty$ control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.

• 전기학회논문지
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• 제56권3호
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• pp.600-603
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• 2007

We propose a method to estimate the asymptotic stability region(ASR) of a mismatched uncertain variable structure system with a bounded controller. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the quadratic stability of the closed-loop control system in the estimated ASR. We also give a simple LMI-based algorithm for estimating the ASR. Finally, we give a numerical example in order to show the effectiveness of our method.

• 제어로봇시스템학회논문지
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• 제11권1호
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• pp.13-18
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• 2005

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.