Stability of x(t)=Ax(t)+Bx(t- tau )

Mori, Takahide; Kokame, Hideki

doi:10.1109/9.28025

Cited by 190 publications

(47 citation statements)

References 12 publications

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“…With the previous states included in the controller (7) One approach to controlling time delay systems is the use of linear matrix inequalities (LMI) techniques. The stability criteria can be either delay independent or delay dependent (i.e., stability is only assured below a particular threshold) [12], [13]. In practice, delay-independent systems are not particularly meaningful, as alternative strategies will apply when communication fails or delays exceed some time threshold, e.g., use of the pause counter in AGC or simple voice communications.…”

Section: A Decentralized Load Frequency Controlmentioning

confidence: 99%

Designing the Next Generation of Real-Time Control, Communication, and Computations for Large Power Systems

et al. 2005

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Section: A Decentralized Load Frequency Controlmentioning

confidence: 99%

Designing the Next Generation of Real-Time Control, Communication, and Computations for Large Power Systems

et al. 2005

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“…Then if there exist P > 0, Q > 0, V > 0, and W such that (3) where then the system is asymptotically stable. In this case, the Lyapunov function can be constructed as (4) where…”

Section: Journal Of Low Frequency Noise Vibration and Active Controlmentioning

confidence: 99%

A Delay-Dependent Stability Criterion for Vibrating Control Systems with LMI Approach

Pan

Wang

Yan

et al. 2003

Journal of Low Frequency Noise, Vibration and Active Control

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This paper provides a new stability criterion for vibrating systems with timeinvariant uncertain delays. Based on an improved upper bound for the inner product of two vectors, a new delay-dependent robust stability criterion is derived. The maximal value of time delay can be obtained by using the LMI control toolbox of Matlab. According to the new method, the maximal delay varying with the parameters of the system is discussed for an SDOF system and the optimal value of the weighting matrix R is found for an MDOF system respectively. Within the interval of permitted time delay, the classical LQR controller can receive satisfactory effects.

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“…when g = 0, such problem has been studied recently by several authors e.g. Hale [1], Mori and Kokame [8,9], Su, Fong, Tseng [10][11][12]. This paper is to extend their results to the stochastic case but the mathematical techniques employed here are very much different from theirs.…”

Section: Dx(t) = [(A +ā(T))x(t) + (B +B(t − τ ))X(t − τ )]Dt + G(t Xmentioning

confidence: 99%

Robustness of exponential stability of stochastic differential delay equations

Mao

1996

IEEE Trans. Automat. Contr.

173

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Regard the stochastic differential delay equation dx(t)=[(A+Ā(t))x(t)+(B+B(t− τ )) x(t−τ )]dt+g(t,x(t),x(t−τ ))dw(t) as the result of the effects of uncertainty, stochastic perturbation and time lag to a linear ordinary differential equationẋ(t)=(A+B)x(t). Assume the linear system is exponentially stable. In this paper we shall characterize how much the uncertainty, stochastic perturbation and time lag the linear system can bear such that the stochastic delay system remains exponentially stable. The result will also be extended to non-linear systems.

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Stability of x(t)=Ax(t)+Bx(t- tau )

Cited by 190 publications

References 12 publications

Designing the Next Generation of Real-Time Control, Communication, and Computations for Large Power Systems

Designing the Next Generation of Real-Time Control, Communication, and Computations for Large Power Systems

A Delay-Dependent Stability Criterion for Vibrating Control Systems with LMI Approach

Robustness of exponential stability of stochastic differential delay equations

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