• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.3
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• pp.63-70
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• 2013

Many real world optimization problems are discrete and multi-valued. Meta heuristics including Genetic Algorithm and Particle Swarm Optimization have been effectively used to solve these multi-valued optimization problems. However, extensive comparative study on the performance of these algorithms is still required. In this study, performance of these algorithms is evaluated with multi-modal and multi-dimensional test functions. From the experimental results, it is shown that Discrete Particle Swarm Optimization (DPSO) provides better and more reliable solutions among the considered algorithms. Also, additional experiments shows that solution quality of DPSO is not lowered significantly when bit size representing a solution increases. It means that bit representation of multi-valued discrete numbers provides reliable solutions instead of becoming barrier to performance of DPSO.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.580-585
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• 1999

This paper deals with the stability of discrete time linear systems with time varying delays in state. In this paper, the magnitude of time-varying delays is assumed to be upper-bouded. The stability of discrete time linear systems with time-varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

• Journal of Korea Society of Industrial Information Systems
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• v.23 no.1
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• pp.53-63
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• 2018

In this paper, we analyze the waiting time of a queueing system with D-BMAP (discrete-time batch Markovian arrival process) and D-policy. Customer group or packets arrives at the system according to discrete-time Markovian arrival process, and an idle single server becomes busy when the total service time of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state waiting time distribution is derived in the form of a generating function. Mean waiting time is derived as a performance measure. Simulation is also performed for the purpose of verification and validation. Two simple numerical examples are shown.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.4
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• pp.305-317
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• 2011

This paper presents an overview on flutter boundary prediction in tests which is principally based on a system stability measure, named Jury's stability criterion, defined in the discrete-time domain, accompanied with the use of autoregressive moving-average (AR-MA) representation of a sampled sequence of wing responses excited by continuous air turbulences. Stability parameters applicable to two-, three- and multi-mode systems, that is, the flutter margin for discrete-time systems derived from Jury's criterion are also described. Actual applications of these measures to flutter tests performed in subsonic, transonic and supersonic wind tunnels, not only stationary flutter tests but also a nonstationary one in which the dynamic pressure increased in a fixed rate, are presented. An extension of the concept of nonstationary process approach to an analysis of flutter prediction of a morphing wing for which the instability takes place during the process of structural morphing will also be mentioned. Another extension of analytical approach to a multi-mode aeroelastic system is presented, too. Comparisons between the prediction based on the digital techniques mentioned above and the traditional damping method are given. A future possible application of the system stability approach to flight test will be finally discussed.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.11 no.6
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• pp.57-63
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• 1997

Uninterruptible power supply(UPS) system should provide a good quality and stable power supply no matter what the condition of the raw mains. And when the mains fails, it must provide uninterrupted power to the load for a specified time. In this paper. discrete control system is introduced to improve output waveforms of UPS. This technique can be obtained output voltage by discrete data of synchronous control and voltage control to various loac. And then, the compact and light UPS can be realized by remove of the analog circuit and simulation and ezperinentation were performed with this control algofihtm. The experiment result show the effectiveness of proposed UPS system uwing the discrete control techjique.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.22 no.2
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• pp.162-168
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• 2008

In this paper, the RCF(Resistive Companion Form) analysis method is applied to analyze small signal stability of power systems including thyristor controlled FACTS(Flexible AC Transmission System) equipments such as TCSC(Thyristor Controlled Series Capacitor). The eigenvalue sensitivity analysis algorithm in discrete systems based on the RCF analysis method is presented and applied to the power system including TCSC. As a result of simulation, the RCF analysis method is very useful to precisely calculate the variations of eigenvalues or newly generated unstable oscillation modes after periodic switching operations of TCSC. Also the eigenvalue sensitivity analysis method based on the RCF analysis method enabled to precisely calculate eigenvalue sensitivity coefficients of controller parameters about the dominant oscillation mode after periodic switching operations in discrete systems. These simulation results are different from those of the conventional continuous system analysis method such as the state space equation and showed that the RCF analysis method is very useful to analyze the discrete power systems including periodically operated switching equipments such as TCSC.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.6
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• pp.792-797
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• 2011

This paper discusses the application of a hybrid discretiziation method for the discretization procedure that needs to be included in discrete particle swarm optimization (DPSO) for the problem of allocating PV (photovoltaic) systems onto distribution power systems. For this purpose, this paper proposes a rule-based expert system considering the objective function value and its optimizing speed as the input parameters and applied it to the PV allocation problem including discrete decision variables. For multi-level discretization, this paper adopts a hybrid method combined with a simple rounding and sigmoid funtion based 3-step and 5-step quantization methods, and the application of the rule based expert system proposing the adequate discretization method at each PSO iteration so that the DPSO with the hybrid discretization can provide better performance than the previous DPSO.

• Journal of Advanced Navigation Technology
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• v.26 no.6
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• pp.504-509
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• 2022

In this paper, we deal with the stability condition of linear time-varying interval discrete systems with time-varying delays and unstructured uncertainty. For the time-varying interval discrete system which has interval matrix as its system matrices, time-varying delay time within some interval value and unstructured uncertainty which can include non-linearity and be expressed by only its magnitude, the stability condition is proposed. Compared with the previous result derived by using a upper bound solution of the Lyapunov equation, the new result is derived by the form of simple inequality based on Lyapunov stability condition and has the advantage of being more effective in checking stability. Furthermore, the proposed condition is very comprehensive, powerful and inclusive the previously published conditions of various linear discrete systems, and can be expressed by the terms of magnitudes of the time-varying delay time and uncertainty, and bounds of interval matrices. The superiority of the new condition is shown in the derivation, and the usefulness and advantage of the proposed condition are examined through numerical example.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.7
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• pp.484-489
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• 1988

Sufficient conditions concerning the perturbation region of system parameters, which guarantee the asymptotic stability of linear time- varying systems, are presented. These conditions are obtained by Lyapunov function approach for continuous-time and discrete-time systems. Also, a computational algorithm using nonlinear programming is proposed for finding the maximum perturbation region which satisfies the sufficient condition for the continuous-time systems. The technique of finding the solution for the continuous-time systems can also be applied to the discrete-time systems. In the continuous-time case, it is shown by an example that the method proposed in this paper yields much larger perturbation region of parameters than other previously reported results. An example of the perturbation region of system paramters for the discrete-time system is also given.