H∞ control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

2017 ◽  
Vol 30 (6) ◽  
pp. 1293-1315 ◽  
Author(s):  
Yuhong Wang ◽  
Zhiteng Pan ◽  
Yan Li ◽  
Weihai Zhang
Keyword(s):  
Time Delay ◽  
Multiplicative Noise ◽  
Markov Systems

Impact of Time Delay and Cross-Correlated Gaussian Colored Noises on Dynamical Characteristics and Stochastic Resonance for a Metapopulation System

2020 ◽  
pp. 2150024
Author(s):  
Kang-Kang Wang ◽  
De-Cai Zong ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Resonant Peak ◽  
Noise Correlation ◽  
Ecological Stability ◽  
Correlation Times ◽  
Correlation Strength

In this paper, the regime shift behaviors between the prosperous state and the extinction state and stochastic resonance (SR) phenomenon for a metapopulation system subjected to time delay and correlated Gaussian colored noises are investigated. Through the numerical calculation of the modified potential function and the stationary probability density function (SPDF), one can make clearly the following results: Both multiplicative noise and noise correlation times can improve effectively the ecological stability and prolong the survival time of the system; while additive noise, time delay and noise correlation strength can weaken significantly the biological stability and speed up the extinction of the population. As for the signal-to-noise ratio (SNR), it is found that time delay, multiplicative noise and noise correlation strength can all impair the SR effect. Conversely, the two noise correlation times and additive noise are in favor of the improvement of the peak values of SNR. It is particularly worth mentioning that in the case of [Formula: see text], time delay [Formula: see text] and self-correlation time [Formula: see text] of the additive noise display exactly the opposite effect on the stimulation of the resonant peak in the SNR–[Formula: see text] plots.

STOCHASTIC RESONANCE IN A TIME-DELAYED BISTABLE SYSTEM WITH COLORED COUPLING BETWEEN NOISE TERMS

2012 ◽  
Vol 26 (30) ◽  
pp. 1250149 ◽  
Author(s):  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Coupling Strength ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Bistable System ◽  
Initial Condition

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with colored coupling between multiplicative and additive noise terms is investigated. The SR can be induced by the multiplicative noise, the time delay and the coupling strength between noise terms. Meanwhile, the SR is affected by the initial condition of the system.

SIMULATION STUDY OF NOISE-ENHANCED STABILITY AND RESONANT ACTIVATION IN A BISTABLE SYSTEM INDUCED BY TIME DELAY

2011 ◽  
Vol 25 (02) ◽  
pp. 141-149 ◽  
Author(s):  
CHUN LI ◽  
LUCHUN DU ◽  
DONGCHENG MEI
Keyword(s):  
Time Delay ◽  
Thermal Activation ◽  
Multiplicative Noise ◽  
Bistable System ◽  
Peak Structure ◽  
Activation Rate ◽  
Linear Delay ◽  
Resonant Activation ◽  
Correlated Noises ◽  
Enhanced Stability

The thermal activation problem of a bistable system driven by correlated noises with time delay is investigated by means of numerical simulations. The simulation results indicate: (1) For the case of the bistable system with linear delay, the phenomenon of noise enhanced stability (NES) is enforced by increasing delay time τ as the multiplicative noise intensity D is smaller, but is weakened as D is larger. (2) For the case of the bistable system with cubic delay, the NES becomes faintness as τ increases. (3) For the case of the bistable system with global delay, the NES is still restrained by increasing τ with smaller D, and in some circumstances, the activation rate as a function of τ exists a peak structure, which demonstrating the emergence of resonant activation.

scholarly journals Construction of Adaptive Consensus Gains for Multiagent Systems with Multiplicative Noise

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shoubo Jin ◽  
Qiuju Yu
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Directed Graph ◽  
Multiplicative Noise ◽  
Communication Delay ◽  
Mean Square ◽  
Inaccurate Information ◽  
Leader Following ◽  
The Mean ◽  
Mean Square Consensus

The leader-following consensus of linear multiagent systems with multiplicative noise and adaptive gains is investigated under the fixed directed graph. Because of multiplicative noise, the agents interacting with the leader can only obtain the inaccurate information. Firstly, this paper designs the adaptive gains of multiagent systems, which can converge to some fixed values and force the states to synchronize. Different from the mandatory gains, the adaptive gains depend on the states of agents and can be adjusted with the change of states. Secondly, it is shown that the multiagent systems without time delay can obtain mean square consensus under the adaptive gains. Moreover, in the presence of multiplicative noise and communication delay, the mean square consensus is also acquired in the same adaptive gains. Finally, the validity of the conclusion is simulated by an example.

scholarly journals H∞Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ming Gao ◽  
Weihai Zhang ◽  
Zhengmao Zhu
Keyword(s):  
Time Delay ◽  
General Class ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Control Design ◽  
Mean Square ◽  
Nonlinear Stochastic Systems ◽  
Numerical Examples

This paper studies the infinite horizonH∞control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean squareH∞control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.

Impact of Time Delay and Non-Gaussian Noise on Stochastic Resonance and Stability for a Stochastic Metapopulation System Driven by a Multiplicative Periodic Signal

2019 ◽  
Vol 18 (03) ◽  
pp. 1950017
Author(s):  
Kang-Kang Wang ◽  
Hui Ye ◽  
Ya-Jun Wang ◽  
Ping-Xin Wang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
Periodic Signal ◽  
Population System ◽  
The Stability ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

Stochastic Dynamical Behaviors for a Time-Delayed Insect Outbreak System with a Periodic Signal Subjected to Multiplicative and Additive Noises

2018 ◽  
Vol 17 (03) ◽  
pp. 1850025
Author(s):  
Kang-Kang Wang ◽  
Lin Ju ◽  
Zu-Run Xu ◽  
Sheng-Hong Li ◽  
Jian-Cheng Wu
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
The Other ◽  
Periodic Signal ◽  
Insect Growth ◽  
Double Peaks ◽  
Growth System ◽  
The Stability

In this paper, our aim is to investigate the steady state behaviors, the stochastic resonance (SR) phenomenon and the mean decline time for a biological insect growth system induced by the terms of time delay, the multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can both weaken the stability of the biological system and accelerate the depression process of the insect population, while time delay can strengthen the stability of the insect growth system and prolong the lifetime of the insect system. With respect to the SR phenomenon caused by time delay, noise terms and the weak periodic signal, the results show that some interesting dual peak phenomena for the signal-to-noise ratio (SNR) occur frequently. Specific contents are as follows: In SNR-[Formula: see text] plots, the additive noise intensity [Formula: see text] and time delay [Formula: see text] can easily induce the phenomenon of dual peaks, while in the SNR-[Formula: see text] plots, the multiplicative noise intensity [Formula: see text] and time delay [Formula: see text] can both reduce the SR effect distinctly. On the other hand, in the SNR-[Formula: see text] plots, when either of [Formula: see text] or [Formula: see text] takes a big value, the other plays a negative role in stimulating the SR phenomenon; while either of them takes a small value, the other can excite a significant effect of double peaks.

Dynamics of Globally Coupled Rotators with Multiplicative Noise

1998 ◽  
Vol 08 (05) ◽  
pp. 915-919
Author(s):  
Seunghwan Kim ◽  
Seon Hee Park ◽  
Chang Soo Ryu ◽  
Seung Kee Han
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Steady States ◽  
Initial Condition ◽  
Delay Effect ◽  
Rotator Model ◽  
Switching Phenomenon ◽  
Time Delay Effect ◽  
Coupled Rotators

We study the dynamics of globally coupled rotator model with multiplicative noise concentrating on time-delay effect. It is shown that at a critical noise intensity the system undergoes a noise-induced transition and is split into clusters. Time-delayed interaction in the system affects the picture of the transition suppressing the clustering of the rotators and generates the switching phenomenon between the clusters. For some values of delay time the system has two stable steady states which show different dynamics. According to the initial condition the system evolves into one of the stable steady states. We discuss the nature of the transition and the switching phenomenon in the system.

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