• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.169-172
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• 1999

In this paper, piecewise quadratic Lyapunov functions are used to analyze the stability of fuzzy-model-based controller. We represent the nonlinear system using a Takagi-Sugeno fuzzy model, which represent the given nonlinear system by fuzzy inference rules and local linear dynamic models. The proposed stability analysis technique is developed by dividing the whole fuzzy system into the smaller separate fuzry systems to reduce the conservatism. Some necessary and sufficient conditions for the proposed method are obtained. Finally, stability of the closed system with various kinds of controller for TS fuzzy model is checked through the proposed method.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.1
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• pp.17-22
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• 1997

The stability robustness problem of linear discrete-time systems with time-varying perturbations is considered. By using Lyapunov direct method, the perturbation bounds for guaranteeing the quadratic stability of the uncertain systems are derived. In the previous results, the perturbation bounds are derived by the quadratic equation stemmed from Lyapunov method. In this paper, the bounds are obtained by a numerical optimization technique. Linear matrix inequalities are proposed to compute the perturbation bounds. It is demonstrated that the suggested bound is less conservative for the uncertain systems with unstructured perturbations and seems to be maximal in many examples. Furthermore, the suggested bound is shown to be maximal for the special classes of structured perturbations.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.458-463
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• 1997

In this paper, we propose a variable structure control approach for the system with matched and unmatched uncertainty. By using time-varying sliding mode, the reaching mode is removed, and the design methodology represents a realistic design approach with quadratic criterion for systems incorporating both matched and unmatched uncertainties. The criterion contains states and linear part of input for all time. The practical application of the control strategy is presented in the design of a stability augmentation system for an aircraft is presented.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.467-476
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• 2017

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• Journal of The Korean Society of Grassland and Forage Science
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• v.41 no.3
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• pp.155-161
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• 2021

This study was conducted to estimate the effect of different cutting lengths on fermentation characteristics and aerobic stability of whole crop rice (WCR) silage. The WCR was harvested at the yellow ripe stage (43.7%, DM), and then cut at 5 (R05), 10 (R10), and 20 cm (R20) of the theoretical length of cut with no cut WCR (R60). Each forage was ensiled into 20 L mini bucket silo (5 kg) for 150 days in quadruplicates. The cutting lengths were not affected the chemical compositions of WCR silage (p > 0.05). The pH (p < 0.001) and concentration of ammonia-N (p = 0.022) in WCR silage were increased linearly with the increase of cutting length. The concentration of lactate had quadratic effect (p = 0.007), which was highest in R20 silage (p < 0.05). The concentration of acetate was increased linearly (p = 0.014), but the concentration of butyrate was decreased linearly (p = 0.033). The lactic acid bacteria count was decreased linearly (p = 0.017), and yeast count had quadratic effect (p = 0.009), which was the highest in R20 silage (p < 0.05). Aerobic stability had strong quadratic effect (p < 0.001), which was the highest in R20 silage (p < 0.05). In conclusion, R60 silage had highest pH by a linear increase of ammonia-N concentration and led to low aerobic stability. While R20 silage had the lowest pH by high lactate concentration and led to high aerobic stability.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.729-733
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• 1988

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problems (LQ-problem) is proposed. In LQ problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired area for good responses as well as for stability and values of the quadratic cost functional are kept less then a specified value. The closed loop systems constructed by this method have merits of LQ problems as well as those of pole assignment problems. Taking into consideration that little is known about the relationship among the quadratic weights, the poles and the values of cost functional, this procedure is also interesting from the theoretical point of view.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.473-486
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• 2015

In this paper, we investigate a stability problem for a functional equation f(-x - y - z) - f(x + y) - f(y + z) - f(x + z) + 2f(x) + 2f(y) + 2f(z) - f(-x) - f(-y) - f(-z) = 0 by applying the direct method.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.543-554
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• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).