• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.777-786
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• 1999

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

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

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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• pp.226-231
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• 2008

In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.83-85
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• 1995

A technique for power system' stabilization is presented using the variable structure control theory. The selection problem of the proper switching vector is very important subject for a design of the variable structure controller. In this paper, the switching vector is selected by desired eigenvalues allocation. and these desired eigenvalues are determined by eigenvalue assignment. Simulation results show that eigenvalue allocation variable structure stabilizer yields better dynamic performance than the others (conventional PSS, optimal linear stabilizer) and is robust to wide variations of the system parameters.

• International Journal of Control, Automation, and Systems
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• v.5 no.1
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• pp.86-92
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• 2007

In this paper, we first establish $D_L$-admissibility and $D_R$-admissibility conditions for singular systems. The admissibility conditions expressed as Lyapunov type inequalities extend the existed results of normal systems to singular systems. As special cases the admissibility conditions of the continuous-time and the discrete-time singular systems can be obtained directly. The results established in this paper can be applied to solve the problems of eigenvalue assignment, regional pole-placement and robust control etc.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.185-188
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• 2005

This paper suggests a control method for efficient topology/parameter evolution in a bond-graph-based GP design framework that automatically synthesizes designs for multi-domain, lumped parameter dynamic systems, We adopt a hierarchical breeding control mechanism with fitness-level-dependent differences to obtain better balancing of topology/parameter search - biased toward topological changes at low fitness levels, and toward parameter changes at high fitness levels. As a testbed for this approach, an eigenvalue assignment problem, which is to find bond graph models exhibiting minimal distance errors from target sets of eigenvalues, was tested and showed improved performance for various sets of eigenvalues.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1264-1271
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• 1999

In this paper, an efficient method of analysis and design of fault detection filter is presented. Since the directional constraint is applied to the eigenstructure associated with the detection space, an eigenvector is determined by the eigenvalues associated with other eigenvectors. Further, the assignment of a pair of eigenvalue and eigenvector leads to the fixation of overall eigenstructure related with the detection space. Using the transmission zeros and the transmission zero vectors, these phenomenon are clearly proven, and an efficient algorithm for design of the fault detection filters is presented.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.2
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• pp.125-138
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• 2001

고유진동수와 감쇠비는 지진이나 바람과 같은 동적 횡하중에 대해 구조물의 응답을 결정하는 주요한 특성이다. 본 연구는 지진하중에 대하여 목표응답 수준을 만족하는 구조물의 고유진동수와 감쇠비를 지정하고, 이 값을 실현하는 점탄성 감쇠기 파라미터의 처적분포를 구하는 설계방법을 제안한다. 여기서 지정할 고유진동수와 감쇠비는 목표응답 수준을 만족하는 여러 조합 중 설계조건과 원래 건물의 특성에 따라 결정될 수 있다. 제안한 설계방법은 점탄성 감쇠기의 감성 파라미터를 고유값의 기울기 정보를 바탕으로 분포시키므로 최적 위치와 크기에 대한 정보를 동시에 제공한다. 예제로서 평면 10층 전단 건물을 대상으로 최적설계를 수행하여 지정된 고유값을 실현하는 파라미터의 최적분포를 구하고 이를 통해 제안한 최적 설계의 특성을 확인하였다. 또한 더 나아가 3차원 일방향 비대칭 전단전물에 제안된 최적설계를 수행하여 그에 대한 적용가능성을 확인하였다.