Stability of stochastic interval systems with time delays

Mao, Xuerong; Selfridge, Colin

doi:10.1016/s0167-6911(00)00103-1

Cited by 33 publications

(23 citation statements)

References 9 publications

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Section: Introductionmentioning

confidence: 99%

“…In fact, the stochastic perturbations can not be avoided either [6,7,10,11,12,21] . On the other hand, the system is unavoidable uncertainty, which is due to the existence of modeling errors, can also destroy the stability of the neural networks.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, the stability analysis problem of neural networks with time-delay has been attracted a large amount of research interest and many sufficient conditions have been proposed to guarantee the asymptotic or exponential stability for the neural networks with various type of time delays such as constant, timevarying, or distributed. see for example [2], [4], [12][13][14][15][16][17][18][19][20] and [24], and the references therein.Though the theoretical research on neural network has made great progress since it was born, but in many networks, such as in electronic neural networks, time delay can not be avoided. In fact, the stochastic perturbations can not be avoided either [6,7,10,11,12,21] .…”

mentioning

confidence: 99%

“…see for example [2], [4], [12][13][14][15][16][17][18][19][20] and [24], and the references therein.…”

mentioning

confidence: 99%

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Robust Mean Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-delays

Liu¹,

Han²

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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-The problem of robust mean-square exponential stability for a class of stochastic interval cellular neural networks with time-delays is investigated. Firstly, a kind of equivalent description of this stochastic interval delayed cellular neural networks is presented. Then by using theÎto formula, Razumikhin theorems, Lyapunov function and norm inequalities, several simple sufficient conditions are obtained which guarantee the robust meansquare exponential stability of the stochastic interval cellular neural networks. and some recent results reported in the literatures are generalized.Index Terms -Robust Mean Square, Neural Networks, Timedelays. I . IntroductionIn recent years, neural networks have been extensively investigated, and successfully applied in many areas such as combinatorial optimization, signal processing, pattern recognition and many other fields. However, all successful applications are greatly dependent on the dynamic behaviors of neural networks. As is well-known now, stability is one of the main properties of neural networks, which is a crucial feature in the design of neural networks. On the other hand, axonal signal transmission delays often occur in various neural networks, and may cause undesirable dynamic network behaviors such as oscillation and instability. Up to now, the stability analysis problem of neural networks with time-delay has been attracted a large amount of research interest and many sufficient conditions have been proposed to guarantee the asymptotic or exponential stability for the neural networks with various type of time delays such as constant, timevarying, or distributed. see for example [2], [4], [12][13][14][15][16][17][18][19][20] and [24], and the references therein.Though the theoretical research on neural network has made great progress since it was born, but in many networks, such as in electronic neural networks, time delay can not be avoided. In fact, the stochastic perturbations can not be avoided either [6,7,10,11,12,21] . On the other hand, the system is unavoidable uncertainty, which is due to the existence of modeling errors, can also destroy the stability of the neural networks. So it is very important to discuss the stability and robustness of cellular network against such error and fluctuation [8,12,14] .To overcome this difficulty, we will discuss the stability problem for a kind of stochastic interval cellular neural networks with time-delays (SICNND), and derive several exponential stability criteria for the cellular neural networks(SICNND). This paper is organized as follows. In section 2, model description of the stochastic interval cellular neural networks with time-delays (SICNND), nomenclatures and lemma are given. In section 3, a kind of equivalent description of this stochastic interval delayed cellular neural networks and the idea for mean-square exponential stability are presented, and a set of some sufficient conditions is derived for the exponential stability of the stochastic interval cellular neural networks system. Finally, th...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…see for example [2], [4], [12][13][14][15][16][17][18][19][20] and [24], and the references therein.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Robust Mean Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-delays

Liu¹,

Han²

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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“…Several conditions for determining the asymptotic stability regions in the controller parameter space have been studied [4] [5]. These approaches are based on the Lyapunov theory and LMI (Linear Matrix Inequality) [6] [7]. An alternative approach to the problem of stabilizing plants with time delay was described in [8].…”

mentioning

confidence: 99%

Moment stability in mean square of stochastic delay differential equation

Xue

Yamamoto

Ikei

2011

2011 Chinese Control and Decision Conference (CCDC)

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Abstract-In this paper, we derive a moment stability region in terms of coefficient parameters for a stochastic delay differential equation. Such a stochastic delay equation with both time delay and random effects is an essential model of control systems. As a main result, a fundamental stability problem is solved by delay-dependent stochastic analysis. We adopt the domain-subdivision approach and use Ito's formula in the analysis. For a given time delay, the stability of the stochastic delay differential equation is studied with variable power of noise. It is also shown that an unstable stochastic delay system become stable by an appropriate power of noise. The main results are illustrated by several numerical solutions of the stochastic delay model.

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Robust Adaptive Control of Uncertain Stochastic Hamiltonian Systems with Time Varying Delay

Sun¹

2015

Asian Journal of Control

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This paper investigates the robust adaptive control problem for a class of time‐delay stochastic Hamiltonian systems. The system under study involves stochastics, parameter uncertaintiess, and time varying delay. The aim of this study is to design an uncertainty‐independent adaptive control law such that, for all admissible uncertainties, as well as stochastics, the closed‐loop Hamiltonian system is robustly asymptotically stable in mean square. Sufficient conditions are proposed to guarantee the rationality and validity of the proposed control laws, which are derived based on Lyapunov functional method. The performance of the controllers is validated through digital simulations.

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Stability of stochastic interval systems with time delays

Cited by 33 publications

References 9 publications

Robust Mean Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-delays

Robust Mean Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-delays

Moment stability in mean square of stochastic delay differential equation

Robust Adaptive Control of Uncertain Stochastic Hamiltonian Systems with Time Varying Delay

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