• Title, Summary, Keyword: uncertain linear time-varying system

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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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Guaranteed Cost Control for Discrete-time Linear Uncertain Systems with Time-varying Delay (시변 시간지연을 가지는 이산 선형 불확실성 시스템에 대한 보장 비용 제어)

  • Kim, Ki-Tae;Cho, Sang-Hyun;Lee, Sang-Kyung;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.6
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    • pp.20-26
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    • 2002
  • This paper deals with the guaranteed cost control problems for a class of discrete-time linear uncertain systems with time-varying delay. The uncertain systems under consideration depend on time-varying norm-bounded parameter uncertainties. We address the existence condition and the design method of the memoryless state feedback control law such that the closed loop system not only is quadratically stable but also guarantees an adequate level of performance for all admissible uncertainties. Through some changes of variables and Schur complement, It is shown that the sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

The robust control for a linear time-varying system using state transformation (상태 변환을 이용한 선형 시변 시스템에 대한 강건한 제어)

  • Cho, Do-Hyeoun;Lee, Sang-Hyo
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.1
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    • pp.1-9
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    • 1998
  • This paper is focussed on the problem of robustly stabilizing a transformable linear time-varying system. The considered system is a class of state feedback transformable linear systems. First, the real linear time-varying system is transformed into the linear time invariant system composed with the time-invariant linear part and the time-varying uncertainty part. Second, the solution to a quadratic stabilization problem in the transformed linear system is give via' Lyapunov methods. Then this solution is used to construct a stabilizing linear control law for the real linear time-varying system.

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Delay-dependent Stability Criteria for Uncertain Stochastic Neural Networks with Interval Time-varying Delays (구간 시변 지연이 존재하는 불확실 확률적 뉴럴 네트웍의 지연의존 안전성 판별법)

  • Kwon, Oh-Min;Park, Ju-Hyun;Lee, Sang-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.11
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    • pp.2066-2073
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    • 2008
  • In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.

New Delay-dependent Stability Criteria for Uncertain Stochastic Systems with Time-varying Delays (시변 지연이 존재하는 불확실 스토캐스틱 시스템의 지연의존 안정성)

  • Kwon, Oh-Min;Park, Ju-Hyun;Lee, Sang-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.58 no.11
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    • pp.2261-2265
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    • 2009
  • In this paper, the problem of delay-dependent stability of uncertain stochastic systems with time-varying delay is considered. The uncertainties are assumed to be norm-bounded. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system are derived in terms of LMI(linear matrix inequality). Two numerical examples are given to show the effectiveness of proposed method.

Static Output Feedback Robust $H\infty$ Fuzzy Control of Discrete-Time Nonlinear Systems with Time-Varying Delay (시변 지연 이산 시간 비선형 시스템에 대한 정적 출력 궤환 $H\infty$ 퍼지 강인 제어기 설계)

  • Kim Taek Ryong;Park Jin Bae;Joo Young Hoon
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.149-152
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    • 2005
  • In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.

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Static Output Feedback Robust $H_{\infty}$ Fuzzy Control of Nonlinear Systems with Time-Varying Delay (시변 지연이 있는 비선형 시스템에 대한 $H_{\infty}$ 퍼지 강인제어기 설계)

  • Kim, Taek-Ryong;Park, Jin-Bae;Joo, Young-Hoon
    • Proceedings of the KIEE Conference
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    • pp.379-381
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    • 2004
  • In this paper, a robust $H_{\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H_{\infty}$ controllers are given in terms of linear matrix inequalities.

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Novel Results for Global Exponential Stability of Uncertain Systems with Interval Time-varying Delay

  • Liu, Yajuan;Lee, Sang-Moon;Kwon, Oh-Min;Park, Ju H.
    • Journal of Electrical Engineering and Technology
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    • v.8 no.6
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    • pp.1542-1550
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    • 2013
  • This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

QFT Parameter-Scheduling Control Design for Linear Time- varying Systems Based on RBF Networks

  • Park, Jae-Weon;Yoo, Wan-Suk;Lee, Suk;Im, Ki-Hong;Park, Jin-Young
    • Journal of Mechanical Science and Technology
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    • v.17 no.4
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    • pp.484-491
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    • 2003
  • For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear. time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.

RBF Network Based QFT Parameter-Scheduling Control Design for Linear Time-Varying Systems and Its Application to a Missile Control System (시변시스템을 위한 RBF 신경망 기반의 QFT 파라미터계획 제어기법과 alt일 제어시스템에의 적용)

  • 임기홍;최재원
    • 제어로봇시스템학회:학술대회논문집
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    • pp.199-199
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    • 2000
  • Most of linear time-varying(LTV) systems except special cases have no general solution for the dynamic equations. Thus, it is difficult to design time-varying controllers in analytic ways, and other control design approaches such as robust control have been applied to control design for uncertain LTI systems which are the approximation of LTV systems have been generally used instead. A robust control method such as quantitative feedback theory(QFT) has an advantage of guaranteeing the stability and the performance specification against plant parameter uncertainties in frozen time sense. However, if these methods are applied to the approximated linear time-invariant(LTI) plants which have large uncertainty, the designed control will be constructed in complicated forms and usually not suitable for fast dynamic performance. In this paper, as a method to enhance the fast dynamic performance, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks for LTV systems with bounded time-varying parameters.

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