• 대한수학회보
• /
• 제53권2호
• /
• pp.541-550
• /
• 2016

In this paper, we introduce a quasi-Banach algebra of infinite matrices, which is inverse-closed in the Banach algebra B(${\ell}^2$) of all bounded operators on ${\ell}^2$.

• Transactions on Control, Automation and Systems Engineering
• /
• 제2권1호
• /
• pp.31-39
• /
• 2000

We present a robust and reliable H$\infty$ state-feedback controller design for linear uncertain systems, which have norm-bounded time-varying uncertainty in the state matrix, and their prespecified sets of actuators are susceptible to failure. These controllers should guarantee robust stability of the systems and H$\infty$ norm bound against parameter uncertainty and/or actuator failures. Based on the linear matrix inequality (LMI) approach, two state-feedback controller design methods are constructed by formulating to a set of LMIs corresponding to all failure cases or a single LMI that covers all failure cases, with an additional costraint. Effectiveness and geometrical property of these controllers are validated via several numerical examples. Furthermore, the proposed LMI frameworks can be applied to multiobjective problems with additional constraints.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제54권1호
• /
• pp.17-25
• /
• 2005

This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

• International Journal of Precision Engineering and Manufacturing
• /
• 제5권3호
• /
• pp.77-84
• /
• 2004

A robust optimal control design is proposed in this study for rigid robotic systems under the unknown loads and the other uncertainties. The uncertainties are reflected in the performance index, where the uncertainties are bounded for the quadratic square of the states with a positive definite weighting matrix. An iterative algorithm is presented for the determination of the weighting matrix required for necessary robustness. Computer simulations have been done for a weight-lifting operation of a two-link manipulator and the simulation results shows that the proposed algorithm is very effective for a robust control of robotic systems.

• International Journal of Control, Automation, and Systems
• /
• 제6권1호
• /
• pp.15-23
• /
• 2008

This paper considers the problem of delay-dependent guaranteed cost controller design for uncertain neutral systems with distributed delays. The system under consideration is subject to norm-bounded time-varying parametric uncertainty appearing in all the matrices of the state-space model. By constructing appropriate Lyapunov functionals and using matrix inequality techniques, a state feedback controller is designed such that the resulting closed-loop system is not only robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. Furthermore, a convex optimization problem is introduced to minimize a specified cost bound. By matrix transformation techniques, the corresponding optimal guaranteed controller can be obtained by solving a linear matrix inequality. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed approach.

• 대한수학회보
• /
• 제46권1호
• /
• pp.117-123
• /
• 2009

This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.

• 전자공학회논문지SC
• /
• 제46권5호
• /
• pp.22-28
• /
• 2009

본 논문에서는 다중 상태 시변 시간지연을 가지는 연속시간 특이시스템의 $H_{\infty}$ 필터링 문제를 다룬다. 제안하는 필터의 목적은 필터링 오차 특이시스템(filtering error singular system)이 정규성, 임펄스 프리, 점근적 안정성 및 $H_{\infty}$ 노옴 유계(bound)를 만족하는 선형 필터를 설계하는 것이다. 먼저, 다중 상태 시변 시간지연을 가지는 특이시스템에 대한 새로운 지연종속 유계실수정리(bounded real lemma)를 자승 요소를 기초로 하는 유한 합 부등식(finite sum inequality)을 이용하여 제안하고, 이로부터 $H_{\infty}$ 필터가 존재할 조건과 필터의 설계기법을 최적화가 가능한 선형행렬부등식(linear matrix inequality)으로 제시한다. 마지막으로 예제를 통하여 제안한 필터 설계 알고리듬의 타당성을 확인한다.

• 대한수학회지
• /
• 제47권6호
• /
• pp.1269-1282
• /
• 2010

We in this note consider a new concept, so called $\pi$-McCoy, which unifies McCoy rings and IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and upper (lower) triangular matrix rings, but the class of $\pi$-McCoy rings contain upper (lower) triangular matrix rings and many kinds of full matrix rings. We first study the basic structure of $\pi$-McCoy rings, observing the relations among $\pi$-McCoy rings, Abelian rings, 2-primal rings, directly finite rings, and ($\pi-$)regular rings. It is proved that the n by n full matrix rings ($n\geq2$) over reduced rings are not $\pi$-McCoy, finding $\pi$-McCoy matrix rings over non-reduced rings. It is shown that the $\pi$-McCoyness is preserved by polynomial rings (when they are of bounded index of nilpotency) and classical quotient rings. Several kinds of extensions of $\pi$-McCoy rings are also examined.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제14권7호
• /
• pp.3057-3075
• /
• 2020

End-to-end network delay plays an vital role in distributed services. This delay is used to measure QoS (Quality-of-Service). It would be beneficial to know all node-pair delay information, but unfortunately it is not feasible in practice because the use of active probing will cause a quadratic growth in overhead. Alternatively, using the measured network delay to estimate the unknown network delay is an economical method. In this paper, we adopt the state-of-the-art matrix completion technology to better estimate the network delay from limited measurements. Although the number of measurements required for an exact matrix completion is theoretically bounded, it is practically less helpful. Therefore, we propose an online adaptive sampling algorithm to measure network delay in which statistical leverage scores are used to select potential matrix elements. The basic principle behind is to sample the elements with larger leverage scores to keep the traits of important rows or columns in the matrix. The amount of samples is adaptively decided by a proposed stopping condition. Simulation results based on real delay matrix show that compared with the traditional sampling algorithm, our proposed sampling algorithm can provide better performance (smaller estimation error and less convergence pressure) at a lower cost (fewer samples and shorter processing time).

• 한국정밀공학회지
• /
• 제23권6호
• /
• pp.88-95
• /
• 2006

In this paper, the gain-scheduled control design proposed in the previous paper has been applied to a target tracking system. In such system, it is needed to attenuate disturbance effectively as long as control input satisfies the given constraint on its magnitude. The scheduled gains are derived in the framework of linear matrix inequality(LMI) optimization by means of the MatLab toolbox. Its effectiveness is verified along with the simulation results compared with the conventional optimum constant gain and the scheduled gain control with constant Q matrix cases.