Exponential Stability of Linear Delay Impulsive Differential Equations

Anokhin, A.; Berezansky, Leonid; Braverman, Elena

doi:10.1006/jmaa.1995.1275

Cited by 133 publications

(85 citation statements)

References 12 publications

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“…(14) is UGES and ξ(t) ≤ √ M ξ t0 e − λ 2 (t−t0) for all t ≥ t 0 . The previous lemma, combined with the work presented in [12], results in the following theorem.…”

Section: A L P -Stability With Bias Of Impulsive Delay Lti Systemsmentioning

confidence: 79%

Stabilizing transmission intervals for Networked Control Systems with nonlinear delay dynamics

Tolić

Hirche²

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper, we consider a nonlinear delay process to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced phenomena such as sampled, distorted and delayed data as well as scheduling protocols. Maximally Allowable Transfer Interval (MATI) labels the greatest transmission interval for which a prescribed Lp-gain, as a measure of control performance, is attained. The proposed methodology combines impulsive delay system modeling with Lyapunov-Razumikhin techniques to allow for communication delays greater than MATIs. Other salient features of our methodology are the consideration of nonuniform variable delays and employment of model-based estimators to prolong MATIs. The present stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols such as Round Robin (RR) and Try-Once-Discard (TOD). Finally, a nonlinear example is provided to demonstrate the benefits of our methodology.

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“…(14) is UGES and ξ(t) ≤ √ M ξ t0 e − λ 2 (t−t0) for all t ≥ t 0 . The previous lemma, combined with the work presented in [12], results in the following theorem.…”

Section: A L P -Stability With Bias Of Impulsive Delay Lti Systemsmentioning

confidence: 79%

Stabilizing transmission intervals for Networked Control Systems with nonlinear delay dynamics

Tolić

Hirche²

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

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“…So the theory of impulsive differential equations is also attracting much attention in recent years [13][14][15][16][17][18][19]. Correspondingly, a lot of stability results of impulsive stochastic functional differential equations have been obtained [20][21][22][23][24][25][26].…”

Section: Dx(t) = F (X T T R(t))dt + G(x T T R(t))dω(t)mentioning

confidence: 99%

Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

Pan

Cao

2012

Adv Differ Equ

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In this article, by using Razumikhin-type technique, we investigate pth moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several stability theorems of impulsive hybrid stochastic functional differential equations are derived. It is assumed that the state variables on the impulses can relate to the finite delay. These new results are employed to a class of n-dimensional linear impulsive hybrid stochastic systems with bounded time-varying delay. Moreover, an effective M-matrix method is introduced to study the exponential stability of these hybrid systems. Meanwhile, some examples and simulations are given to show our results.

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“…H 1 The function f 1 satisfies the Lipschitz condition: there exists a positive constant L 1 > 0 such that…”

Section: Preliminariesmentioning

confidence: 99%

The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type

Chen

Zhang

Zhao

2010

Advances in Difference Equations

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By applying the Banach fixed point theorem and using an inequality technique, we investigate a kind of random impulsive integrodifferential equations of neutral type. Some sufficient conditions, which can guarantee the existence, uniqueness, and exponential stability in mean square for such systems, are obtained. Compared with the previous works, our method is new and our results can generalize and improve some existing ones. Finally, an illustrative example is given to show the effectiveness of the proposed results.

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Exponential Stability of Linear Delay Impulsive Differential Equations

Cited by 133 publications

References 12 publications

Stabilizing transmission intervals for Networked Control Systems with nonlinear delay dynamics

Stabilizing transmission intervals for Networked Control Systems with nonlinear delay dynamics

Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type

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