• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.95-99
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• 1993

In this paper, we discuss H$_{\infty}$ robust performance problem for uncertain system described in a descriptor form. We show that the method based on Riccati equation can be extended to solve this problem. First, such a sufficient condition is given that the system described in a descriptor form is quadratic stable and H$_{\infty}$ norm of a specified transfer function is less than a given level. Using this result, a state feedback law which ensures H$_{\infty}$ robust performance of closed loop system is derived based on a positive definite solution of a Riccati equation. This result shows that a solution of the problem can be also obtained by solving H$_{\infty}$ standard problem for an extended plant. Finally, a design example and simulation results will be given.ven.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• 대한수학회논문집
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• 제35권2호
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.296-298
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• 1992

Presented in this paper is a generalized norm bound for the continuous and discrete algebraic Riccati equations. The generalized norm bound provides a lower bound of the Riccati solutions specified by any kind of submultiplicative matrix norms including the spectral, Frobenius and $\ell_1$ norms.

• Coupled systems mechanics
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• 제2권3호
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• pp.255-269
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• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• 대한전기학회논문지
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• 제33권12호
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• pp.491-496
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• 1984

The optimal control and filtering problems for the systems with the generalized state space model are considered and the generalized Riccati equation is derived. Also the algorithm for the solution of the generalized algebraic Riccati equation is developed and it is shown that the algotithm can be applied to the case where the matrix R is singular or near singular.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.425-427
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• 1993

Some upper bounds for the solution of the continuous algebraic Riccati equation are presented. These consist of bounds for summations of eigenvalues, products of eigenvalues, individual eigenvalues and the minimum eigenvalue of the solution matrix. Among these bounds, the first three are the first results for the upper bound of each case, while bounds for the minimum eigenvalue supplement the existing ones and require no side conditions for their validities.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 D
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• pp.2082-2084
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• 2003

A practical real-time LOS rate estimator is proposed to handle the time-varying measurement noise statistics. To calculate the optimal Kalman gain, the algebraic transformation method is taken into account. By using the algebraic transformation, the differential algebraic Riccati equation(DARE) regarding estimation error covariance is replaced by the simple algebraic Riccati equation(ARE). The proposed LOS estimation filter gain is only a function of relative range. Consequently, the proposed method is computationally very efficient and suitable for embedded environment.

• 제어로봇시스템학회논문지
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• 제18권12호
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• pp.1086-1089
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• 2012

We propose a near optimal controller design method for ramp metering based on SDRE (State Dependent Riccati Equation) approach. We parameterize the optimal nonlinear controller in terms of the solution matrices of an SDRE. We also give a simple algorithm to obtain the controller gain. Finally we give numerical results to show the effectiveness of the proposed near optimal traffic controller design method.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.133-147
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• 2006

In this paper, by using the Riccati transformation technique we establish some new oscillation criteria for second-order nonlinear perturbed dynamic equation on time scales. An example illustrating our main results is also given.