• Journal of the Korean Society for Precision Engineering
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• v.22 no.4
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.67-76
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• 2009

We show the existence of at least two nontrivial solutions for a class of the systems of the nonlinear elliptic equations with Dirichlet boundary condition under some conditions for the nonlinear term. We obtain this result by using the variational linking theory in the critical point theory.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.105-107
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• 1991

A chemical process model represented by partial differential equations was studied as one of nonlinear distributed parameter control problems. Using an optimal control theory in the form of maximum principles based on nonlinear integral equations, an algorithm to solve the problem was developed and coded into a computer program.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.4
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• pp.61-68
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• 2001

A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.145-149
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• 1987

The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Earthquakes and Structures
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• v.11 no.1
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• pp.129-140
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• 2016

This paper presents He's Energy Balance Method (EBM) for solving nonlinear oscillatory differential equations. Three strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with numerical solutions using Runge-Kutta's algorithm. The effects of different important parameters on the nonlinear response of the systems are studied. The results show the presented method is potentially to solve high nonlinear vibration equations.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.4
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• pp.379-387
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• 1999

In general, solving or analyzing nonilinear dynamical equations is very difficult and requires special techniques. To avoid these difficulties, systems are generally linearized in an attempt to predict their begavior. These linearized equations, however, may not predict true system behavior. Therefore, the nonlinear dynamical analysis using bifurcation theory may become a fundamental framework in understanding nonlinear situation in power systems. In this paper, we propose a systematic procedure based on a bifurcation theory to analyze nonlinear behaviors in power systems. We show usefulness of our procedure by applying 3-bus model system. In addition, we consider nonlinear model of SMES and verify the effect of SMES in power system's nonlinear behaviors.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].