• Computational Structural Engineering
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• v.10 no.4
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• pp.251-265
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• 1997

A piecewise-linear system is utilized to model the offshore mooring system. The approximated piecewise-linear restoring force is obtained to be compared with the analytically derived restoring force of a mooring system. Two systems are compared to verify the applicability of the piecewise-linear system to evaluate responses of the mooring system. Using the piecewise-linear system, the response behaviors of mooring systems are examined under various excitations. Nonlinearity of the system and effects of both system and excitation parameters are intensively examined. System responses are identified mainly by observing Poincare maps. The mooring system is found to have various types of responses such as regular harmonic, subharmonic and complex nonlinear behaviors, including chaos by utilizing a piecewise-linear system. Various values of parameters are applied to determine the effects of parameters upon system responses. Response domains are determined by establishing parametric maps.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.533-533
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• 2000

Stabilization of piecewise-linear systems with unknown switching information is presented. The current subsystem is identified from the output, and the identified subsystem is used for the observer-based control. The stability of the overall system is proven and the performance is evaluated via a simulation.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.459-472
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• 2012

A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dynamics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We finally present some numerical examples of the bifurcation phenomena in the system.

• Journal of Power Electronics
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• v.11 no.3
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• pp.327-334
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• 2011

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.133-136
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• 2004

This paper proposes a stability condition in 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).

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.2012-2015
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• 2002

Synchronization phenomena of chaos observed in a dual-structured system is presented. The system is consisting of two identical piecewise-linear systems and the simple coupling between the two systems enables the synchronization of the chaotic behavior. An application of the proposed dual-structure to a real power system for the parameter value identification is also presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.461-467
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• 2000

Mechanical problems are basically three dimensional nonlinear dynamic problems, which makes it difficult to solve. The difficulties are tried to overcome by modeling, i.e., simplifications of the system with the assumptions or negligence of minute effects. However, the correctness or usefulness of the model should be verified through the comparison with experimental results, which is the process of physical understanding of the system. The understanding of physics of the system make it possible to design or operation of the system. The effects of clearance and friction are always difficult problems in mechanical system due to its nonlinearity. The nonlinearity comes from piecewise-linear characteristics of the stiffness and damping of the system. The modeling of piecewise-linearity and the experimental result are discussed in this paper for impact and friction oscillator and rotor rubbing problem, which is the combination of impact and friction problems.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.33.1-33
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• 2001

We address a novel approach to identify a nonlinear dynamic system for Wiener models, which are composed of a linear dynamic system part followed by a nonlinear static part. The aim of system identification here is to provide the optimal mathematical model of both the linear dynamic and the nonlinear static parts in some appropriate sense. Assuming the nonlinear static part is invertible, we approximate the inverse function by a piecewise linear function. We estimate the piecewise linear inverse function by using the evolutionary computation approach such as genetic algorithm (GA) and evolution strategies (ES), while we estimate the linear dynamic system part by the least squares method. The results of numerical simulation studies indicate the usefulness of proposed approach to the Wiener model identification.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.1122-1127
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• 2003

Typical application of detecting piecewise-linear curves includes vectorizing of scanned drawings whirh is a vital step in installing any geographic information system. This paper considers the problem of optimally approximating a piecewise linear curve to a set of digital points while satisfying given intersection angles between each pair of neighboring lines. The criterion for optimality is to minimize the sum of squared deviations. The problem is formulated as an unconstrained nonlinear programming model. An algorithm which guarantees an optimal solution is then proposed and its validity is tested with both a synthetically generated image and a real image. The test results illustrate the excellent performance of the proposed algorithm.