• International Journal of Control, Automation, and Systems
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• 제5권5호
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• pp.594-600
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• 2007

A sufficient condition for the robust D-stability of dynamic interval systems is proposed in this paper. This D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of matrix inequalities defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as previous results. This condition is also extended to the robust D-stabilization problem of dynamic interval systems, which supplies an effective synthesis procedure for any LMI D-region. The proposed conditions can be simplified to a set of LMIs, which can be solved by efficient interior point methods in polynomial time.

• Structural Engineering and Mechanics
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• 제44권1호
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• pp.73-84
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• 2012

This paper strongly addresses to the problem of the mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find sharp bounds of the structural parameters for infilled frame system modeled with finite element method. Infill walls are generally treated as non-structural elements considerably to improve the lateral stiffness, strength and ductility of the structure together with the frame elements. Because of their complex nature, they are often neglected in the analytical model of building structures. However, in seismic design, ignoring the effect of infill wall in a numerical model does not accurately simulate the physical behavior. In this context, there are still some uncertainties in mechanical and also geometrical properties in the analysis and design procedure of infill walls. Structural uncertainties can be studied with a finite element formulation to determine sharp bounds of the structural parameters such as wall thickness and Young's modulus. In order to accomplish this sharp solution as much as possible, interval finite element approach can be considered, too. The structural parameters can be considered as interval variables by using the interval number, thus the structural stiffness matrix may be divided into the product of two parts which correspond to the interval values and the deterministic value.

• 대한수학회지
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• 제54권6호
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• pp.1667-1682
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• 2017

In this paper, the Hermitian positive definite solutions of the matrix equation $X^s+A^*X-^tA=Q$, where Q is an $n{\times}n$ Hermitian positive definite matrix, A is an $n{\times}n$ nonsingular complex matrix and $s,t{\in}[1,{\infty})$ are discussed. We find a matrix interval which contains all the Hermitian positive definite solutions of this equation. Also, a necessary and sufficient condition for the existence of these solutions is presented. Iterative methods for obtaining the maximal and minimal Hermitian positive definite solutions are proposed. The theoretical results are illustrated by numerical examples.

• Structural Engineering and Mechanics
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• 제21권2호
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• pp.185-204
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• 2005

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of the stability of vibration control systems with uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of eigenvalues of the close-loop system with uncertain parameters is presented. The lower bounds of eigenvalues can be used to estimate the robustness of the stability the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.

• 한국항행학회논문지
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• 제21권6호
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• pp.608-613
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• 2017

본 논문에서는 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 지연 상태변수에 존재하는 불확실성 안정범위에 관한 것을 다룬다. 고려된 시스템은 지연 없는 상태변수에 대한 시스템 행렬이 구간범위에서 시변으로 변동하고, 지연 시간이 구간범위 내에서 시변인 지연 상태변수에 대하여 비구조화된 불확실성이 시변으로 존재하는 시스템이다. 기존의 많은 연구들이 시변에 대한 부분을 고려하지 못하고 시불변 경우에 대하여 얻어진 것에 반하여, 본 논문에서는 모든 요소를 시변으로 고려하여 새로운 안정범위를 도출하였다. 새로운 안정범위는 적용 가능한 시스템에 대한 제한이 없는 것으로 그 효용성이 기존의 결과 보다 우수하다. 제안된 범위는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 이용하는 복잡한 과정이 필요하지 않다. 수치예제를 통하여 제안된 결과가 기존의 결과들을 포함할 수 있음을 보이고, 이들 보다 확장성과 효용성이 우수함을 확인한다.

• 한국경영과학회지
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• 제19권2호
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• pp.75-84
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• 1994

The uncertainty in the relative weights of a pairwise comparison matrix n Multi-attribute Decision Making (MADM) is caused by imprecise preference information of decision maker. In this paper, it is shown how weight of attributes can be derived from the pairwise comparison matrix with interval pairwise comparison. The preference information of each pair of attributes with a point pairwise comparison is combined with an interval pairwise comparison in order to estimate a point pairwise comparison for a pair of attributes with the imprecise preference information. A numerical example shows the suggested procedure for deriving weights of attributes.

• Journal of Power Electronics
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• 제16권5호
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• pp.1781-1790
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• 2016

This study focuses on the coordination control problem of multiple electrical excited synchronous motor systems. A robust coordination controller is designed on the basis of cross coupling and an interval matrix. The proposed control strategy can deal with load uncertainty. In addition, the proposed control strategy is applied to a high-power metal-rolling system. Simulation and experiment results demonstrate that the proposed control strategy achieves good dynamic and static performance. It also shows better coordination performance than traditional proportional-integral controllers.

• 동력기계공학회지
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• 제20권2호
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• pp.5-16
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• 2016

Generally, methods using transfer techniques, like the transfer matrix method and the transfer stiffness coefficient method, find natural frequencies using the sign change of frequency determinants in searching frequency region. However, these methods may omit some natural frequencies when the initial frequency interval is large. The Sylvester-transfer stiffness coefficient method ("S-TSCM") can always obtain all natural frequencies in the searching frequency region even though the initial frequency interval is large. Because the S-TSCM obtain natural frequencies using the number of natural frequencies existing under a searching frequency. In this paper, the algorithm for the free vibration analysis of axisymmetric conical shells was formulated with S-TSCM. The effectiveness of S-TSCM was verified by comparing numerical results of S-TSCM with those of other methods when analyzing free vibration in two computational models: a truncated conical shell and a complete (not truncated) conical shell.

• 통합자연과학논문집
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• 제10권1호
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• pp.33-39
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

• 통합자연과학논문집
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• 제13권4호
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• pp.152-157
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• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.