• Title/Summary/Keyword: Lyapunov matrix equation

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Dynamic Instability of Lattice-Dome Structures by Lyapunov Concept

  • Han, Sang-Eul;Hou, Xiao-Wu
    • Architectural research
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    • v.10 no.1
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    • pp.25-32
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    • 2008
  • Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method to study parametrical instability of lattice dome structures, which is subjected to harmonically pulsating load. We consider elastic stiffness and geometrical stiffness simultaneously during the calculation of stiffness matrix, and adopt consistent mass matrix to make the solution more correct. In order to obtain instability regions, we represent displacements and accelerations in dynamic equation by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability regions eventually. Finally, we take 24-bar star dome and 90-bar lamella dome as examples to investigate dynamic instability phenomena.

A Switching Controller for Stabilization of Uncertain Linear Systems (불확실한 선형시스템의 안정화를 위한 스위칭제어기)

  • Kim, Jung-Soo;Kim, Byung-Yeun;Lyon, Joon
    • Proceedings of the KIEE Conference
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    • 1991.11a
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    • pp.382-385
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    • 1991
  • In order to stabilize linear time-invariant systems with the unknown system matrix, a piecewise constant linear state feedback control law including switching logic is developed. A number of feedback gain matrices are first precomputed by solving the Algebraic Riccati Equation with prescribed degree of stability, and then are switched over in a direction to increase degree of stability. Switching stops when a Lyapunov function shows the decreasing property, and hence switching times are finite.

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The SOC, Capacity-fade, Resistance-fade Estimation Technique using Sliding Mode Observer for Hybrid Electric Vehicle Lithium Battery (하이브리드 자동차용 리튬배터리의 충전량, 용량감퇴, 저항감퇴 예측을 위한 슬라이딩 모드 관측기 설계)

  • Kim, Il-Song;Lhee, Chin-Gook
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.5
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    • pp.839-844
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    • 2008
  • A novel state of health estimation method for hybrid electric vehicle lithium battery using sliding mode observer has been presented. A simple R-C circuit method has been used for the lithium battery modeling for the reduced calculation time and system resources due to the simple matrix operations. The modeling errors of simple model are compensated by the sliding mode observer. The design methodology for state of health estimation using dual sliding mode observer has been presented in step by step. The structure of the proposed system is simple and easy to implement, but it shows robust control property against modeling errors and temperature variations. The convergence of proposed observer system has been proved by the Lyapunov inequality equation and the performance of system has been verified by the sequence of urban dynamometer driving schedule test. The test results show the proposed observer system has superior tracking performance with reduced calculation time under the real driving environments.

A New Consideration for Discrete-System Reduction via Impulse Response Gramian

  • Younseok Choo;Park, Jaeho
    • International Journal of Control, Automation, and Systems
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    • v.2 no.3
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    • pp.384-389
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    • 2004
  • Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix$A_r$ of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices $b_r$ and $c_r$ are obtained so that various initial Markov parameters and time-moments of the original system are preserved in the reduced model. In this paper a different approach is presented based on the recursive relationship among the impulse response Gramians.

Design of H Repetitive Control Systems using State Feedback (상태 궤환을 이용한 H 반복 제어 시스템 설계)

  • Doh, Tae-Yong
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.1
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    • pp.6-11
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    • 2014
  • Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.

Sampled-Data Controller Design for Nonlinear Systems Including Singular Perturbation in Takagi-Sugeno Form (특이섭동을 포함한 타카기 - 수게노 형태의 비선형 시스템을 위한 새로운 샘플치 제어기의 설계기법 제안)

  • Moon, Ji Hyun;Lee, Jaejun;Lee, Ho Jae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.26 no.1
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    • pp.50-55
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    • 2016
  • This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

Observer Design for Linear Neutral Systems with Time-Varying Delays (시변 시간 지연을 포함하는 선형 뉴트럴 시스템의 관측기 설계)

  • Song, Min-Kook;Joo, Young-Hoon;Park, Jin-Bae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.4
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    • pp.483-487
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    • 2007
  • This paper is concerned with the observer design problem for linear neutral systems with time-varying delays. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both observer analysis and design problems are investigated. Sufficient conditions for a linear neutral system to be stable are first established. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedure.

Stability Bound for Time-Varying Uncertainty of Time-varying Discrete Interval System with Time-varying Delay Time (시변 지연시간을 갖는 이산 구간 시변 시스템의 시변 불확실성의 안정범위)

  • Han, Hyung-seok
    • Journal of Advanced Navigation Technology
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    • v.21 no.6
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    • pp.608-613
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    • 2017
  • In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

Stability Condition for Discrete Interval Time-varying System with Time-varying Delay Time (시변 지연시간을 갖는 이산 구간 시변 시스템의 안정조건)

  • Han, Hyung-seok
    • Journal of Advanced Navigation Technology
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    • v.20 no.5
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    • pp.475-481
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    • 2016
  • In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

Stability Condition for Discrete Interval Time-Varying System with Unstructured Uncertainty and Time-Varying Delay Time (비구조화된 불확실성과 시변 지연시간을 갖는 이산 시변 구간 시스템의 안정조건)

  • Hyung-seok Han
    • 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.