• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.435-450
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• 2004

We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of $n_{\infty}$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.11
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• pp.895-900
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• 2005

We derive a linear matrix inequality(LMI) condition guaranteeing that any invariant zeros of a triple (A, B, C) lie in the open left half plane of the complex plane, i.e. $C(sI-A)^{-1}B$ is minimum phase. The LMI condition is equivalent to a certain constrained Lyapunov matrix equation which can be found in many results relating to stability analysis or control design. We show that the LMI condition can be used to simplify various control engineering problems such as a dynamic output feedback control problem, a variable structure static output feedback control problem, and a nonlinear system observer design problem. Finally, we give some numerical examples.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.1-28
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• 2000

In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, We give a new proof of the Himmelberg fixed point theorem and G-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.293-296
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• 2006

This paper presents new sufficient conditions to an intelligent digital redesign (IDR). The purpose of the IDR is to effectively convert an existing continuous-time fuzzy controller to an equivalent sampled-data fuzzy controller in the sense of the state-matching. The state-matching error between the closed-loop trajectories is carefully analyzed using the integral quadratic functional approach. The problem of designing the sampled-data fuzzy controller to minimize the state-matching error as well as to guarantee the stability is formulated and solved as the convex optimization problem with linear matrix inequality (LMI) constraints.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1823-1830
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• 2016

Let H and K be two Hilbert spaces, and let A and B be two bounded linear operators from H to K. We are interested in $RangeB^*{\supseteq}RangeA^*$. It is well known that this is equivalent to the inequality $A^*A{\geq}{\varepsilon}B^*B$ for a positive constant ${\varepsilon}$. We study conditions in terms of symbols when A and B are singular integral operators, Hankel operators or Toeplitz operators, etc.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1197-1200
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• 1996

This paper is concerned with the design of robust state feedback controller for a class of linear time-delay systems with norm-bounded nonlinear uncertainties. Under the proposed delay-independent criterion, asymptotic stability for the system is investigated using the conventional Lyapunov method. Moreover, the robust controller can be obtained by solving the linear matrix inequality which is equivalent to the suggested conditions.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.623-630
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• 2009

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.

• Journal of Korean Society of Transportation
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• v.24 no.2 s.88
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• pp.169-178
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• 2006

Traffic assignment has been used both for predicting travel demands and for evaluating the tools for alleviating congestion on road network in advance. Some assignment models have been proposed such as equivalent mathematical minimization method, variational inequality problem, nonlinear complementary problem and fixed point method, in following the principle of Wardrop (1952) that no driver can not Improve his travel cost by unilaterally changing his route. Recently Jin(2005a) presented a traffic assignment model based on dynamic process. This paper proposes a solution algorithm for the model of Jin and assesses the performances. Compared to the Frank-Wolfe method, which has been wildly used for solving the existing assignment models, the proposed algorithm is expected to be more efficient because it does not need to evaluate the objective function. Two numerical examples are used for assessing the algorithm, and they show that the algorithm converges to user equilibrium of Wardrop.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.5
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• pp.617-623
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• 2010

In this research an LMI based mixed $H_2/H_{\infty}$ controller for a Wheeled Inverted Pendulum is designed and a numerical simulation of that is carried out. The Wheeled Inverted Pendulum is a kind of an inverted pendulum that has two equivalent points. To keep that the naturally unstable equivalent point, a controller should control the wheels persistently. Dynamic equations of the Wheeled Inverted Pendulum are derived with considering inclined road that is one of the representative road conditions. A Linear Matrix Inequality method is used to construct a controller that is able to stabilize the Wheeled Inverted Pendulum with considering the inclined road condition aggressively. Various numerical simulations show that the LMI based controller is doing well on not only flat road but also inclined road condition.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.