• 제어로봇시스템학회논문지
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• 제12권4호
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• pp.339-345
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• 2006

An analysis methodology of Decentralized Dynamic Surface Control (DDSC) for the large-scale interconnected nonlinear systems is presented in this paper. While the centralized DSC approach proposed in [14] has a difficulty to check the quadratic stability for the large-scale systems numerically due to dramatic increases of the order of overall augmented error dynamics, DDSC is relatively easy to check the quadratic stability since lower order error dynamics of individual subsystems are used. Then, a systematic procedure for designing DDSC will be developed. Furthermore, after a quadratic function containing a reachable set is defined, it will be calculated numerically to indicate the performance of DDSC in the framework of convex optimization. Finally an illustrative example will be given for showing the advantages of DDSC compared with other decentralized nonlinear control techniques.

• Korean Journal of Mathematics
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• 제19권1호
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• pp.17-24
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• 2011

Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0, and $$2(_{2d-2}C_{d-1}-_{2d-2}C_d)f\({\sum_{j=1}^{2d}}x_j\)+{\sum_{{\iota}(j)=0,1,{{\small\sum}_{j=1}^{2d}}{\iota}(j)=d}}\;f\({\sum_{j=1}^{2d}}(-1)^{{\iota}(j)}x_j\)=2(_{2d-1}C_d+_{2d-2}C_{d-1}-_{2d-2}C_d){\sum_{j=1}^{2d}}f(x_j)$$ for all $x_1$, ${\cdots}$, $x_{2d}{\in}X$, then the even mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Hyers-Ulam stability of the above functional equation in Banach spaces.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 D
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• pp.2516-2518
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• 2004

This paper proposes a stability condition in discrete-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• 한국콘텐츠학회논문지
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• 제2권4호
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• pp.93-98
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• 2002

함수 방정식은 연구원들이 함수 자체의 정확한 형태를 가정하지 않고 단순히 기본적인 함수의 성질만을 언급하는 한정적이지 않은 방정식을 통하여 일반적인 관점의 수학적 형상화를 공식화하는데 매우 중요한 구실을 하기 때문에 실험적인 학문에서 유용하다. 그러한 많은 함수 방정식 가운데에서 이 논문은 다소 일반화된 2차 함수 방정식을 선택해 해를 구하며 이 방정식의 안정성을 증명한다. a$^2$f((x+y/a))+b$^2$f((x-y/b)) = 2f(x)+2f(y)

• Korean Journal of Mathematics
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• 제21권1호
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• pp.1-21
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• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• 대한전기학회논문지:전력기술부문A
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• 제48권5호
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• pp.553-559
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• 1999

The robust control problem of the linear systems with uncertainty is classified as the robust stability problem guaranteeing the stability and the robust performance problem guaranteeing the disired performance. In this paper, we considered the robust performance analysis problem, which find the upper buund of the quadratic performance of the uncertain linear system, and the robust guaranteed performance controller design problem which design a controller guaranteeing the desired quadratic performance. At first, we treated the analysis problem and presented the two results; one is dependent on the performance of the nominal system and another is independent on this. And we treated the design method guaranteeing the desired performance for the uncertain linear systems, Finally, we show the usefulness of our results by numerical examples.

• Journal of Electrical Engineering and Technology
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• 제9권5호
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• pp.1520-1526
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• 2014

This paper presents a probabilistic method to evaluate the total transfer capability (TTC) by considering the sequential quadratic programming and the uncertainty of weather conditions. After the initial TTC is calculated by sequential quadratic programming (SQP), the transient stability is checked by time simulation. Also because power systems are exposed to a variety of weather conditions the outage probability is increased due to the weather condition. The probabilistic approach is necessary to evaluate the TTC, and the Monte Carlo Simulation (MCS) is used to accomplish the probabilistic calculation of TTC by considering the various weather conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• 충청수학회지
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• 제32권3호
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• pp.337-347
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• 2019

In this paper, we investigate the generalized Hyers-Ulam stability of the quadratic and quartic type functional equations $$f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)-2f(kx)\\{\hfill{67}}+2k^2f(x)+2(k^2-1)f(y)=0,\\f(x+5y)-5f(x+4y)+10f(x+3y)-10f(x+2y)+5f(x+y)\\{\hfill{67}}-f(-x)=0,\\f(kx+y)+f(kx-y)-k^2f(x+y)-k^2f(x-y)\\{\hfill{67}}-{\frac{k^2(k^2-1)}{6}}[f(2x)-4f(x)]+2(k^2-1)f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.