• Title, Summary, Keyword: norm-bounded uncertainties

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Robust Stability of Uncertain Discrete-Time Linear Systems with Time-Varying Delays (시변 시간 지연을 갖는 불확실한 이산 시간 선형 시스템의 견실 안정성)

  • Song, Seong-Ho;Park, Seop-Hyeong;Lee, Bong-Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.6
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    • pp.641-646
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    • 1999
  • This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

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Robust H$_\infty$ Control for Discrete Time-delay Linear Systems with Frobenius Norm-bounded Uncertainties (파라미터 불확실성을 가지는 이산 시간지연 시스템에 대한 견실 H$_\infty$ 제어)

  • 김기태;이형호;이상경;박홍배
    • 제어로봇시스템학회:학술대회논문집
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    • pp.23-23
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    • 2000
  • In this paper, we proposed the problems of robust stability and 개bust H$_{\infty}$ control of discrete time-delay linear st.stems with Frobenius norm-bounded uncertainties. The existence condition and the design method of robust H$_{\infty}$ state feedback control]or are given. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

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A Krein Space Approach for Robust Extended Kalman Filtering on Mobile Robots in the Presence of Uncertainties

  • Jin, Seung-Hee;Park, Jin-Bae
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1771-1776
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    • 2003
  • In mobile robot navigation, one of the key problems is the pose estimation of the mobile robot. Although the odometry can be used to describe the motions of the mobile robots quite simple and accurately, the validities of the models are limited by a number of error sources contaminating the encoder outputs so that applying the conventional extended Kalman filter to these nominal model does not yield the satisfactory performance. As a remedy for this problem, we consider the uncertain nonlinear kinematic model of the mobile robot that contains the norm bounded uncertainties and also propose a new robust extended Kalman filter based on the Krein space approach. The proposed robust filter has the same recursive structure as the conventional extended Kalman filter and can hence be readily designed to effectively account for the uncertainties. The computer simulations will be given to verify the robustness against the parameter variation as well as the reliable performance of the proposed robust filter.

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Nonlinear Modification Scheme for Reducing Cautiousness of Linear Robust Control

  • Maki, Midori;Hagino, Kojiro
    • 제어로봇시스템학회:학술대회논문집
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    • pp.108-111
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    • 1999
  • In this paper, we develope a composite control law for linear systems with norm-bounded time-varying parameter uncertainties, which consists of a basic linear robust control do-signed so as to generate a desired transient time-response for the worst-case parameter variation and a nonlinear modification term designed so as to reduce cautiousness of the linear robust control in an adaptive manner. The proposed controller is established such that the reduction of cautiousness of the linear robust control is well incorporated into the achievement of a good transient behavior.

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A New PID Controller with Lyapunov Stability for Regulation Servo Systems

  • Lee, Jung-Hoon
    • Journal of IKEEE
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    • v.13 no.1
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    • pp.11-18
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    • 2009
  • In this paper, the stability of second order uncertain systems with regulation of PID type controllers is analyzed by using Lyapunov second method for the first time in the time domain. The property of the stability of PID regulation servo systems is revealed in sense of Lyapunov, i.e., bounded stability due to the disturbances and uncertainties. By means of the results of this stability analysis, the maximum norm bound of the error from the output without variation of the uncertainties and disturbances is determined as a function of the gains of the PID control, which make it enable to analyze the effect resulted from the variations of the disturbances and uncertainties using this norm bound for given PID gains. Using the relationship of the error from the output without variation of the uncertainties and disturbances and the PID gain with maximum bounds of the disturbances and uncertainties, the robust gain design rule is suggested so that the error from the output without the variation of the disturbances and uncertainties can be guaranteed by the prescribed specifications as the advantages of this study. The usefulness of the proposed algorithm is verified through an illustrative example.

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Robust stabilization of time-delay systems with nonlinear uncertainties

  • Park, Juhyun;Won, Sangchul
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1197-1200
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    • 1996
  • This paper is concerned with the design of robust state feedback controller for a class of linear time-delay systems with norm-bounded nonlinear uncertainties. Under the proposed delay-independent criterion, asymptotic stability for the system is investigated using the conventional Lyapunov method. Moreover, the robust controller can be obtained by solving the linear matrix inequality which is equivalent to the suggested conditions.

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Nonfragile Guaranteed Cost Controller Design for Uncertain Large-Scale Systems (섭동을 갖는 대규모 시스템의 비약성 성능보장 제어기 설계)

  • Park, Ju-Hyeon
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.51 no.11
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    • pp.503-509
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    • 2002
  • In this paper, the robust non-fragile guaranteed cost control problem is studied for a class of linear large-scale systems with uncertainties and a given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties and controller gain variations. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.

Design of Repetitive Control System for Linear Systems with Time-Varying Uncertainties (시변 불확실성을 가지는 선형 시스템을 위한 반복 제어 시스템의 설계)

  • Chung Myung Jin;Doh Tae-Yong
    • Journal of Institute of Control, Robotics and Systems
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    • v.11 no.1
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    • pp.13-18
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    • 2005
  • This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.

Delay-dependent Guaranteed Cost Control for Uncertain Time-delay Systems (불확실 시간지연 시스템에 대한 지연량을 고려한 성능보장 제어)

  • 이영삼;문영수;권욱현
    • 제어로봇시스템학회:학술대회논문집
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    • pp.13-13
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    • 2000
  • This paper considers delay-dependent guaranteed cost control for uncertain time-delay systems with norm-bounded parametric uncertainties. A new delay-dependent condition for the existence of the guaranteed cost control law is presented in terms of linear matrix inequalities (LMI). An algorithm involving convex optimization is proposed to design a controller which guarantees the suboptimal minimum of the guaranteed cost of the closed-loop system for all admissible uncertainties.

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Robust Control for Networked Control Systems with Admissible Parameter Uncertainties

  • Ji, Kun;Kim, Won-Jong
    • International Journal of Control, Automation, and Systems
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    • v.5 no.4
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    • pp.372-378
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    • 2007
  • This paper discusses Robust $H{\infty}$ control problems for networked control systems (NCSs) with time delays and subject to norm-bounded parameter uncertainties. Based on a new discrete-time model, two approaches of robust controller design are proposed. A numerical example and experimental verification with an NCS test bed are given to illustrate the feasibility and effectiveness of proposed design methodologies.