• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.581-584
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• 1998

This paper presents a scheme for fuzzy modelling and control of continuous-time nonlinear systems using a genetic algorithm. A fuzzy model is characterized by fuzzy "if-then" rules whose consequence part has a linear dynamic equation as subsystem of the system. The parameters of the fuzzy model are adjusted by a genetic algorithm. Then a tracking controller which guarantees stability of the overall system is designed. The simulation result demonstrates the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2007.10a
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• pp.70-71
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• 2007

This paper presents an application of LQR(Linear Quadratic Regulator) for experimental control moment gyroscope. To be specific, mathematical model is first derived based on the quaternion and Lagrange's equation, state feedback controller using LQR scheme is designed, and to show the stability of the scheme, experimental results are given.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.35 no.2
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• pp.41-48
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• 2023

In this study, simplified linear numerical method that can simulate wave generation and transformation by a moving bottom is introduced. Numerical analysis is conducted in wave number domain after continuity equation, linear dynamic and kinematic free surface boundary conditions and linear kinematic bottom boundary condition are Fourier transformed, and the results are expressed in space domain by an inverse Fourier transform. In the wavenumber domain, the dynamic free water surface boundary condition and the kinematic free water surface boundary condition are numerically calculated, and the velocity potential in the mean water level (z = 0) satisfies the continuity equation and the kinematic bottom boundary condition. Wave generation and transformation are investigated when the triangular and rectangular shape of bottoms move periodically. The results of the simplified numerical method are compared with the results of previous analytical solutions and agree well with them. Stability of numerical results according to the calculation time interval (Δt) and the calculation wave number interval (Δk) was also investigated. It was found that the numerical results were appropriate when Δt ≤ T(period)/1000 and Δk ≤ π/100.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Journal of Advanced Navigation Technology
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• v.22 no.6
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• pp.630-635
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• 2018

In this paper, we consider the stability condition for the linear discrete systems with time-varying delay and unstructured uncertainty. The considered system has time invariant system matrices for non-delayed and delayed state variables, but its delay time is time-varying within certain interval and it is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. In the many previous literatures, the time-varying delay and unstructured uncertainty can not be dealt in simultaneously but separately. In the paper, new stability conditions are derived for the case to which two factors are subjected together and compared with the existing results considering only one factor. The new stability conditions improving many previous results are proposed as very effective inequality equations without complex numerical algorithms such as LMI(Linear Matrix Inequality) or Lyapunov equation. By numerical examples, it is shown that the proposed conditions are able to include the many existing results and have better performances in the aspects of expandability and effectiveness.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.4
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• pp.53-61
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• 1998

This paper describes the stability analysis of TSK (Takagi-Sugeno-Kang) fuzzy systems which can represent a large class of nonlinear systems with good accuracy. A TSK fuzzy model consists of TSK fuzzy rules and the consequent of each fuzzy rule is a linear input-output equation with a constant term. There may exist equilibrium points more than one in the TSK fuzzy model and each equilibrium point rnay also have different nature of stability. The local stability of an equilibrium point is determined by eigenvalues of the Jacobian matrix of the linearized TSK fuzzy model around the equilibrium point. Stability of both the continuous-time and the discrete-time systems is analyzed in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.628-633
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• 1994

A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.483-487
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• 2007

This paper is concerned with the observer design problem for linear neutral systems with time-varying delays. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both observer analysis and design problems are investigated. Sufficient conditions for a linear neutral system to be stable are first established. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedure.

• Transactions of the Korean Society of Automotive Engineers
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• v.14 no.6
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• pp.160-170
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• 2006

If hydraulic pump controlled by mechanical type regulator has more than one control function, the construction of regulator will be very complicated and control performance falls drastically. It is difficult to have more than one control function for hydraulic pump controlled by electronic type hydraulic valve due to the inconsistency of controllers. This paper proposes a multi-function control technique which controls continuously flow, pressure and power by using EPPR(Electronic Proportional Pressure Reducing) valve in swash plate type axial piston pump. Nonlinear mathematical model is developed from the continuity equation for the pressurized control volume and the torque balance for the swash plate motion. To simplify the model we make the linear state equation by differentiating the nonlinear model. A reaction spring is installed in servo cylinder to secure the stability of the control system. We analyze the stability and disturbance by using the state variable model. Finally, we review the control performances of flow, pressure and power by tests using PID controller.