Stochastic stability of interconnected string systems

Socha, L.

doi:10.1016/s0960-0779(03)00266-2

Cited by 17 publications

(31 citation statements)

References 8 publications

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“…The stable parameter regions of the systems in Theorem 1 are much larger than that in Theorem 2 in the paper (Socha 2004) under the same conditions.…”

Section: Remarkmentioning

confidence: 66%

“…The method to determine the stability of systems in the paper (Socha 2004) is essentially based on weighted Lyapunov function method which is difficult to deal with the nonlinear system, and it is generally not applied to the cases of Theorem 1. The method we get is easy to handle the infinite-dimension stochastic interconnected systems with strong nonlinear coupling items.…”

Section: Remarkmentioning

confidence: 99%

“…The controller is designed based on the system stability, so it is necessary to study the stability of infinite-dimension stochastic interconnected systems. Socha (2004) studied a class of interconnected systems with random factors and further established the sufficient conditions of string stability. Based on the Lyapunov weighted function, his method has difficulty in dealing with the strong coupling interconnected systems, especially the infinitedimensional systems.…”

Section: Introductionmentioning

confidence: 99%

“…A criterion for exponential string stability of the systems is obtained. Thus, the problem which can't be solved in the paper (Socha 2004) can be dealt with, and the scope of the parameters of the system stability be expanded. Meanwhile, it is easier to deal with infinitedimensional stochastic interconnected systems with strong coupling items.…”

Section: Introductionmentioning

confidence: 99%

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String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

Shi¹,

Zhang²

2012

International Journal of Systems Science

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The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.

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“…The stable parameter regions of the systems in Theorem 1 are much larger than that in Theorem 2 in the paper (Socha 2004) under the same conditions.…”

Section: Remarkmentioning

confidence: 66%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

Shi¹,

Zhang²

2012

International Journal of Systems Science

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“…It is well known that stochastic disturbance cannot be avoided in real interconnected systems [11][12][13]. Some sufficient conditions for ensuring the exponential string p-stability of a class of weakcoupling vehicle longitudinal following systems with stochastic disturbance were obtained by using vector Lyapunov function method in Ref.…”

Section: Introductionmentioning

confidence: 99%

String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

Zhang

Lan

2013

Journal of Dynamic Systems, Measurement, and Control

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Associated with automatic vehicle following system is the problem of the stability of a platoon of vehicles. The stability with mode constraint is the property of damping disturbances as they travel away from the source in the system. In this paper, a class of infinite-dimensional vehicle longitudinal following system with stochastic disturbance is analyzed. By applying geometrical analysis method, a lemma for analyzing the stability of generalized vector comparison inequalities with respect to the original systems is established. With the help of the lemma, some sufficient conditions for assuring the string exponential stability with mode constraint of the original system are obtained by applying vector Lyapunov function method. The obtained conditions are less conservative than the existing ones. A numerical example is given to show the effectiveness of the established conditions.

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Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Shi¹,

Zhang²,

Xu³

et al. 2015

Asian Journal of Control

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In this paper, the interconnecting structure between a certain system and its lower order subsystems within the infinitedimension stochastic interconnected systems is analyzed. Assuming that the excitations are parametric white noises, the exponential string stability for a few classes of nonlinear stochastic interconnected systems is discussed. By using the vector Lyapunov function method, the sufficient conditions of exponential string stability are derived, expanding the scope of the parameters for systems stability. Moreover, some cases of exponential string stability for vehicle-following systems in automated highway systems are specified. Finally, an example is shown to illustrate the proposed method.

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Stochastic stability of interconnected string systems

Cited by 17 publications

References 8 publications

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

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