Exponential stability for linear time-delay systems with delay dependence

Liu, Pin‐Lin

doi:10.1016/j.jfranklin.2003.10.003

Cited by 69 publications

(45 citation statements)

References 17 publications

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“…As a result of numerical experiment, the system is stable in the region of a corresponding to the negative part of GðA; B; tÞ: The upper bounds of the above example derived from another method are found in the literature [15][16][17]. It is known that the maximum delay to stabilize system (14) is t ¼ 6:1726 according to the analytical results in References [15][16][17], which are obtained via analytic computation.…”

Section: Application and Examplesmentioning

confidence: 93%

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Constrained simulated annealing for stability margin computation in a time‐delay system

Kim

Bae²

2006

Intl J Robust & Nonlinear

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SUMMARYThe stability margin of a time-delay system is formulated via factorization. This paper provides a numerical method for computing the stability margin of time-delay linear time-invariant systems with delay dependence by using a constrained simulated annealing algorithm. The constrained simulated annealing is used to solve a nonlinear continuous constrained optimization problem, which is derived from computing the stability margin of a delay system. Illustrative examples show that the established method can verify the stability for a class of time-delay systems.

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Section: Application and Examplesmentioning

confidence: 93%

“…It is known that the maximum delay to stabilize system (14) is t ¼ 6:1726 according to the analytical results in References [15][16][17], which are obtained via analytic computation. From Figure 1, the proposed method produces the same maximum stability margin as the existing results.…”

Section: Application and Examplesmentioning

confidence: 99%

Constrained simulated annealing for stability margin computation in a time‐delay system

Kim

Bae²

2006

Intl J Robust & Nonlinear

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“…Before proceeding, we recall the following theorem on the exponential stability of time delay system [16]. For the sake of convenience, we adapt the notation in [16] into ours.…”

Section: Topology Design Under Time Delaymentioning

confidence: 99%

“…For the sake of convenience, we adapt the notation in [16] into ours. Consider the time-delay systems (11) utilizing the following transformation…”

Section: Topology Design Under Time Delaymentioning

confidence: 99%

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Communication topology design for large-scale interconnected systems with time delay

Gusrialdi

Hirche

2011

Proceedings of the 2011 American Control Conference

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Abstract-Communication networks provide a larger flexibility with respect to the control design of large-scale interconnected systems by allowing the information exchange between the local controllers of the subsystems. The use of communication networks comes, however, at the price of nonideal signal tranmission such as time delay which is a source of instability and deteriorates the control performance. This paper introduces an approach for the design of the communication topology for the distributed control of large-scale interconnected systems in order to optimize the whole system's performance in the presence of constant time delay. First, a decentralized control law that stabilizes the overall interconnected system is designed. Then the performance is improved by designing the distributed control law, i.e. allowing the controller of the subsystems to exchange information, by considering the time delay in the networks. As a novelty in this paper, the design of the communication topology between the controllers is also considered. The problem is formulated as a mixed-integer optimization problem. Furthermore, a method based on matrix perturbation theory is discussed to design the topology which also captures the relation between the time delay, controller gain and performance of the overall system. In addition, it is shown that the proposed strategy also guarantees the stability of the overall system under the permanent communication link failure. The results are validated through a numerical example.

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Improved exponential estimates for neutral systems

Shu

Lam

2009

Asian Journal of Control

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Improved exponential estimates and a new sufficient condition for the exponential stability of neutral type time‐delay systems are established in terms of linear matrix inequalities (LMIs). A new Lyapunov‐Krasovskii functional candidate with appropriately constructed exponential terms is introduced to prove the exponential stability and to reduce the conservatism. For the uncertain case, a corresponding condition for the robust exponential stability is also given. It is shown by numerical examples that the proposed conditions are less conservative than existing results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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Exponential stability for linear time-delay systems with delay dependence

Cited by 69 publications

References 17 publications

Constrained simulated annealing for stability margin computation in a time‐delay system

Constrained simulated annealing for stability margin computation in a time‐delay system

Communication topology design for large-scale interconnected systems with time delay

Improved exponential estimates for neutral systems

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