• 충청수학회지
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• 제20권4호
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• pp.465-476
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• 2007

The aim of this paper is to investigate the stability problem bounded by function for the generalized sine functional equations as follow: $f(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2\\g(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2$. As a consequence, we have generalized the superstability of the sine type functional equations.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

• Transactions on Control, Automation and Systems Engineering
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• 제3권3호
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• pp.164-169
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• 2001

This paper considers the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all $\varepsilon$$\in$(0, $\infty$). Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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• pp.1094-1097
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• 1993

In this paper, the absolute stability criterion of nonlinear plants with sector bounded nonlinear feedback is derived. The result obtained is useful for applications, in particular, stability analysis and design of fuzzy logic controllers.

• International Journal of Aeronautical and Space Sciences
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• 제14권3호
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• pp.256-263
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• 2013

The saturation of the actuator impairs the response performance of the near space interceptor control system. A control system based on the properties of linear tracking system is designed for this problem. The properties are that the maximum value of the pseudo-Lyapunov function of the linear tracking control system do not present at the initial state but at the steady state, based on which the bounded stability problem is converted into linear tracking problem. The pseudo-Lyapunov function of the linear tracking system contain the input variables; the amplitude and frequency of the input variables affect the stability of the nonlinear control system. Designate expected closed-loop poles area for different input commands and obtain a controller which is function of input variables. The coupling between variables and linear matrices make the control system design problem non-convex. The non-convex problem is converted into a convex LMI according to the Shur complement lemma and iterative algorithm. Finally the simulation shows that the designed optimal control system is quick and accurate; the rationality of the presented design techniques is validated.

• 제어로봇시스템학회논문지
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• 제2권3호
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• pp.158-164
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• 1996

In this paper, we consider the problem of robust stability of discretd time-delay systems subjected to perturbations. Two classes of perturbations are treated. The first one is the nonlinear norm-bounded perturbation, and the second is the structured time-varying parametric perturbation. Based on the discrete-time Lyapunov stability theory, several new sufficient conditions for robust stability of the system are presented. From these conditions, we can estimate the maximum allowable bounds of the perturbations which guarantee the stability. Finally, numerical examples are given to demonstrate the effectiveness of the results.

• 대한수학회지
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• 제36권1호
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• 충청수학회지
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• 제25권1호
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• pp.1-18
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• 2012

The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

• 대한수학회논문집
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• 제29권4호
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.183-200
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• 2012

A two-strain epidemic model with an age structure mutation and varying population is studied. By means of the spectrum theory of bounded linear operator in functional analysis, the reproductive numbers according to the strains, which associates with the growth rate ${\lambda}^*$ of total population size are obtained. The asymptotic stability of the steady states are obtained under some sufficient conditions.