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

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Stability Bounds of Delayed Time-varying Perturbations of Discrete Systems (이산시스템에서 시간지연을 갖는 시변 상태 지연 섭동의 안정 범위에 관한 연구)

  • Lee, Dal-Ho;Han, Hyung-Seok
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.2
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    • pp.147-153
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    • 2007
  • The stability robustness problem of linear discrete-time systems with delayed time-varying perturbations is considered. Compared with continuous time system, little effort has been made for the discrete time system in this area. In the previous results, the bounds were derived for the case of non-delayed perturbations. There are few results for delayed perturbation. Although the results are for the delayed perturbation, they considered only the time-invariant perturbations. In this paper, the sufficient conditions for stability can be expressed as linear matrix inequalities(LMIs). The corresponding stability bounds are determined by LMI(Linear Matrix Inequality)-based algorithms. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed results.

The Transformation Time-invarying Linear System for a Class of Time-varying Linear System via I/O Transformation (입출력 변환을 이용한 선형 시변 시스템의 선형 시불변 변환)

  • Cho, Do-Hyoun;Won, Young-Jin;Cho, Chang-Ho;Lee, Tae-Sick;Lee, Jong-Yong
    • Proceedings of the IEEK Conference
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    • pp.483-484
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    • 2007
  • In this paper, we consider the input-output transformation for the time-varying linear system and get the time-invarying linear system. And we present the necessary sufficient condition for the I/O transformation. The transformed system represent the system with the multiple integral. We verify the proposal algorithm via the example and examine.

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Discrete Variable Structure Control for Linear Time-Varying Systems

  • Park, Kang-Bak;Teruo Tsuji;Tsuyoshi Hanamoto;S. Umerjan
    • 제어로봇시스템학회:학술대회논문집
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    • pp.508-508
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    • 2000
  • In this paper, a discrete-time variable structure controller for linear time-varying systems with time-varying disturbances is proposed. The proposed method guarantees that the system state is globally uniformly ultimately bounded (G,U.U.B.) under the existence of external disturbances.

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Robust adaptive control of linear time-varying systems which are not necessarily slowly varying

  • Song, Chan-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1424-1429
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    • 1990
  • This paper presents an indirect adaptive control scheme for discrete linear systems whose parameters are not necessrily slowly varying. It is assumed that system parameters are modelled as linear combinations of known bounded functions with unknown constant coefficients. Unknown coefficients are estimated using a recursive least squares algorithm with a dead zone and a forgetting factor. A control law which makes the estimated model exponentially stable is constructed. With this control law and a state observer, all based on the parameter estimates, it is shown that the resulting closed-loop system is globally stable and robust to bounded external disturbances and small unmodelled plant uncertainties.

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Stability Bounds of Time-Varying Uncertainty and Delay Time for Discrete Systems with Time-Varying Delayed State (시변 시간지연을 갖는 이산시스템의 시변 불확실성의 안정 범위)

  • Han, Hyung-Seok
    • Journal of Institute of Control, Robotics and Systems
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    • v.18 no.10
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    • pp.895-901
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    • 2012
  • The stability robustness problem of linear discrete systems with time-varying unstructured uncertainty of delayed states with time-varying delay time is considered. The proposed conditions for stability can be used for finding allowable bounds of timevarying uncertainty and delay time, which are solved by using LMI (Linear Matrix Inequality) and GEVP (Generalized Eigenvalue Problem) known as powerful computational methods. Furthermore, the conditions can imply the several previous results on the uncertainty bounds of time-invariant delayed states. Numerical examples are given to show the effectiveness of the proposed algorithms.

H Sampled-Data Control of LPV Systems with Time-varying Delay (시변지연을 가지는 LPV시스템의 H 샘플데이타 제어)

  • Liu, Yajuan;Lee, Sangmoon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.64 no.1
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    • pp.121-127
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    • 2015
  • This paper considers the problem of sampled-data control for continuous linear parameter varying (LPV) systems. It is assumed that the sampling periods are arbitrarily varying but bounded. Based on the input delay approach, the sampled-data control LPV system is transformed into a continuous time-delay LPV system. Some less conservative stabilization results represented by LMI (Linear Matrix Inequality) are obtained by using the Lyapunov-Krasovskii functional method and the reciprocally combination approach. The proposed method for the designed gain matrix should guarantee asymptotic stability and a specified level of performance on the closed-loop hybrid system. Numerical examples are presented to demonstrate the effectiveness and the improvement of the proposed method.

Stability Bound for Time-Varying Uncertainty of Positive Time-Varying Discrete Systems with Time-Varying Delay Time (시변 지연시간을 갖는 양의 시변 이산시스템의 시변 불확실성의 안정범위)

  • Han, Hyung-Seok
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.6
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    • pp.424-428
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    • 2016
  • A simple new sufficient condition for asymptotic stability of the positive linear time-varying discrete-time systems, with unstructured time-varying uncertainty in delayed states, is established in this paper Compared with previous results that cannot be applied to time-varying systems; the time-varying system and delay time are considered simultaneously in this paper. The proposed conditions are compared with suitable conditions for the typical discrete-time systems. The considerations are illustrated by numerical examples of previous work.

Approximation of Linear Time-Varying System Using Wavelet Transform (웨이브렛 변환을 이용한 시변 선형 시스템의 근사화)

  • Lee, Young-Seog;Kim, Dong-Ok;Ahn, Dae-Chan;Seo, Bo-Hyeok
    • Proceedings of the KIEE Conference
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    • pp.717-719
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    • 1997
  • This paper discusses approximate modelling of discrete-time linear time-varying system(LTVS). The wavelet transform is considered as a tool for representing and approximating a LTVS. The joint time-frequency properties of wave analysis are appropriate for describing the LTVS. Simulatly results is included to illustrate the popential application of the technique.

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$H_\infty$ Controller Design for Discrete-time Linear Systems with Time-varying Delays in States using S-procedure (S-procedure를 이용한 상태에 시변 시간지연을 가지는 이산 선형 시스템에 대한 $H_\infty$ 제어기 설계)

  • Kim, Ki-Tae;Cho, Sang-Hyun;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.2
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    • pp.95-103
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    • 2002
  • This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. 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.

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.