• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.621-638
• /
• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• Journal of Institute of Control, Robotics and Systems
• /
• v.15 no.8
• /
• pp.818-822
• /
• 2009

In this paper, we consider a decentralized observer design problem for fault detection in large-scaled linear time-invariant systems. Since the fault detection residual is desired to be sensitive on the fault, we use the H_ index performance criterion. Sufficient conditions for the existence of such an observer is presented in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.125.1-125
• /
• 2001

This paper deals with the eigenvalue assignment technique for linear time-varying systems to achieve feedback stabilization. For this, we introduce the novel eigenvalue concepts. Then, we propose the Ackerman-like formula for linear time-varying systems. It is believed that this technique is the generalized version of the Ackerman formula forlinear time-invariant systems. The advantages of the proposed technique are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.05a
• /
• pp.256-259
• /
• 2000

A new digital redesign method which can construct a digital controller for multiple linear systems is developed. The proposed method utilized the recently developed LMI theory to obtain a single digital controller which provide good state matching properties with multiple linear systems. A numerical example is provided to evaluate the feasibility of the proposed approach.

• KIEE International Transaction on Systems and Control
• /
• v.12D no.1
• /
• pp.39-42
• /
• 2002

This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.4
• /
• pp.511-513
• /
• 2005

We investigate some situations in connection with two exact sequences of fuzzy linear maps.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.2
• /
• pp.113-120
• /
• 2012

In this paper we study various properties of the fuzzy linear maps over the fuzzy quotient spaces. In particular we obtain some exact sequences of the fuzzy linear maps over the fuzzy quotient spaces.

• Atmosphere
• /
• v.24 no.4
• /
• pp.491-502
• /
• 2014

As a part of the KIAPS (Korea Institute of Atmospheric Prediction Systems) Package for Observation Processing (KPOP), we have developed the modules for Advanced Microwave Sounding Unit-A (AMSU-A) pre-processing and its bias correction. The KPOP system calculates the airmass bias correction coefficients via the method of multiple linear regression in which the scan-corrected innovation and the thicknesses of 850~300, 200~50, 50~5, and 10~1 hPa are respectively used for dependent and independent variables. Among the four airmass predictors, the multicollinearity has been shown by the Variance Inflation Factor (VIF) that quantifies the severity of multicollinearity in a least square regression. To resolve the multicollinearity, we adopted simple linear regression and Principal Component Regression (PCR) to calculate the airmass bias correction coefficients and compared the results with those from the multiple linear regression. The analysis shows that the order of performances is multiple linear, principal component, and simple linear regressions. For bias correction for the AMSU-A channel 4 which is the most sensitive to the lower troposphere, the multiple linear regression with all four airmass predictors is superior to the simple linear regression with one airmass predictor of 850~300 hPa. The results of PCR with 95% accumulated variances accounted for eigenvalues showed the similar results of the multiple linear regression.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.1726-1729
• /
• 1997

In general, the solvability of linear robust output regulation problem are not preserved under time-sampling. Thus, it is found that the digital regulator implemented by itme-sampling of anlog output regulator designed based on the continuous-time linear system model is nothing but a 1st order approximation with respect to time-sampling. By the way, one can design an improved sampled-data regulator with respect to sampling time by utilizing the intrinsic structure of the system. In this paper, we study the system structures which it is possible to design an improved sampled-data regulator with respect to sampling time.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.297-303
• /
• 2001

In this paper, the problem of the stability analysis for a class of linear neutral systems with time-varying delay is investigated. Using the Lyapunov method, a delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs) is presented. The LMIs can be easily solved by various convex optimization algorithms.