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Stability of uncertain delay differential equations

Xiao Wang, Yufu Ning
2017 Journal of Intelligent & Fuzzy Systems  
Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations.  ...  At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented.  ...  Acknowledgment This work is supported by Natural Science Foundation of Shandong Province (ZR2014GL002) and Higher Educational Science and Technology Program of Shandong Province (12LN15).  ... 
doi:10.3233/jifs-16639 fatcat:pjvwf4fqxfhkfiase44qfwwwey

Robust stability of uncertain stochastic differential delay equations

Xuerong Mao, Natalia Koroleva, Alexandra Rodkina
1998 Systems & control letters (Print)  
q 8i x | j x ¢ e þ 8 x | e 9f ei $ W x i jp e Wu x i ji y 9 vn jf 9x f i ~ D e 9f ~ G x j W 8x f Ñ 5s Qµ R X c D iù %T $ 9 jf 9x G Öf 9 x 9 $ 8 ei 9 9 x q e r x sÖi j 9x ¢ !  ... 
doi:10.1016/s0167-6911(98)00080-2 fatcat:lnukxxrndbe4rgrg2zamrkwzt4

A New Stability Analysis of Uncertain Delay Differential Equations

Xiao Wang, Yufu Ning
2019 Mathematical Problems in Engineering  
This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability.  ...  Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed.  ...  Acknowledgments This work was funded by National Natural Science Foundation of China (11701338) and a Project of Shandong Province Higher Educational Science and Technology Program (J17KB124).  ... 
doi:10.1155/2019/1257386 fatcat:rqljyqp3kjdcphhmrxcfukktmq

Existence, uniqueness, and stability of uncertain delay differential equations with V-jump

Zhifu Jia, Xinsheng Liu, Cunlin Li
2020 Advances in Difference Equations  
Once more, the concept of stability for uncertain delay differential equations with V-jump is proposed. In addition, the sufficient condition for stability theorem is derived.  ...  No previous study has involved uncertain delay differential equations with jump.  ...  Authors' contributions All authors read and approved the final version of the manuscript.  ... 
doi:10.1186/s13662-020-02895-4 fatcat:uud5uflybbggzjsfniv275mu3y

Partial stabilisation of large-scale discrete-time linear control systems

Peter Benner, Maribel Castillo, Enrique S. Quintana Orti
2005 International Journal of Computational Science and Engineering (IJCSE)  
Yang Asymptotic Stability of Solutions Delay Differential Equations 859 Y. H. Peng Robust Control for The Time-Varying Delay Uncertain Neutral Systems 654 X. G. Yu and B. T.  ...  Gao Stability of Impulsive Differential Equations with Time Delay 745 Y. Zhang and J. Sun Stability of Sampled-Data Systems with Nonequidistant Sampling 753 G.  ... 
doi:10.1504/ijcse.2005.008907 fatcat:7bcwbbhnv5bf7omtgtuz5dhkkm

Qualitative Analysis of Dynamic Activity Patterns in Neural Networks

Ivanka Stamova, Haydar Akca, Gani Stamov
2011 Journal of Applied Mathematics  
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations.  ...  the results of investigation on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations.  ...  This paper presents the simulation of electrical loads from consumers and from a distributed generation (DG) in network nodes in using a neural network method and an algorithm of Feed -forward neural networks  ... 
doi:10.1155/2011/208517 fatcat:k237pc47bzddtitm7f2uuf4abm

Page 5190 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Akhmerov (2-AOSSI-MC) 88j:34156 34K20 92A15 Bélair, Jacques (3-MTRL) Stability of a differential-delay equation with two time lags.  ...  The authors consider the uncertain system of differential dif- ference equations (1) X(t) = Apx(t) + Ai x(t —h) + fo(x(t),t) +  ... 

Page 2470 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
The author presents an overview of the investigation of the stability of delay differential equations by means of quadratic Lyapunov functionals or functions.  ...  (RS-MIEM-CY; Moscow) Stability of nonlinear differential equations with distributed delay. Nonlinear Anal. 34 (1998), no. 7, 1081-1095.  ... 

Page 2950 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
The results obtained are extended to treat the exponential stability of uncertain paramet- ric systems with multiple time-delays.  ...  (KEN-NRB; Nairobi) Periodic solutions of a system of delay differential equations. (English summary) Indian J. Math. 44 (2002), no. 1, 95-117.  ... 

Page 2064 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
The parameter space is then given a topology (which allows the delays tT; to vary), and it is shown that the set of parameter values for which the corresponding system of delay differential equations is  ...  The author studies the following system of delay differential equations: X(t) = A(o},-++,0%)x(t)+ B(t,--+,t%)u(t), where A and B are polynomial matrices in the delay operators.  ... 

Robust Control of Delayed Fin Stabilizer Stochastic Systems of a Ship

Cheung-Chieh Ku, Chin-Yuan Hsu
2018 Proceedings of Engineering and Technology Innovation  
In this paper, the robust control problem of delayed fin stabilizer stochastic system of a ship with uncertainty is discussed and investigated.  ...  By solving the conditions, some feasible solutions can be obtained to establish the controller to guarantee robust stability of the delayed fin stabilizer stochastic system of a ship in the mean square  ...  Acknowledgement This work was supported by the Ministry of Science and Technology, under Contract MOST 106-2221-E-019-006.  ... 
doaj:019c2e6be7e9415cb512e86cd8ca5d63 fatcat:zr2zutf345dvhpvnl7wpkdvwly

Stability of fuzzy control systems with bounded uncertain delays

Zhang Yi, Pheng Ann Heng
2002 IEEE transactions on fuzzy systems  
Conditions for global exponential stability of free fuzzy systems with uncertain delays are derived.  ...  Stability of systems with uncertain delays is interesting since in practical applications it is not easy to know the delays exactly.  ...  Results for global exponential stability of free fuzzy systems with uncertain delays will be given and proved in Section III.  ... 
doi:10.1109/91.983283 fatcat:2yra7knqn5gvdpinqenuxedusq

Finite Dimensional Controller Design for Stabilization of Uncertain Time-Delay Systems

Suthee PHOOJARUENCHANACHAI, Katsuhisa FURUTA
1992 Transactions of the Society of Instrument and Control Engineers  
Furuta: A Riccati Equation Approach to Stabilization of Uncertain Systems with Delayed State, Proceedings of SICE '90, 721/724 (1990) that Define Z:=(Y-1-X)-1.  ...  - ed by linear differential-difference equations of the with initial condition and bounded continuous time delays Here we shall employ the method of Lyapunov functionals7) to identify a  ... 
doi:10.9746/sicetr1965.28.326 fatcat:6pos5erk4zdkthu5gl64uhhkfq

An LMI Approach to Optimal Memoryless Regulator of Systems with Time-Delay in the States and Its Circle Condition
状態にむだ時間を含む系における最適メモリーレスレギュレータのLMIによる構成と円条件

Tomohiro KUBO
2001 Transactions of the Society of Instrument and Control Engineers  
Thowsen: Memoryless Stabilization of Linear Delay-Differential Systems, IEEE Transactions on Automatic Control, AC-26-2, 586/587 (1981) 8) T.  ...  Aldeen: Stabilization of Uncertain Dynamic Delay Systems by Memoryless Feedback Controllers, In- ternational Journal of Control, 59-6, 1525/1542 (1994) 14) H.H. Choi and M.J.  ... 
doi:10.9746/sicetr1965.37.133 fatcat:j6kgwvk7xnbvtacjg2bo7wmvki

New Developments in Time-Delay Systems and Its Applications in Engineering

Guangdeng Zong, Wei Xing Zheng, Ligang Wu, Yang Yi
2013 Mathematical Problems in Engineering  
"Directly solving special second order delay differential equations using Runge-Kutta-Nyström method" by M.  ...  "moment stability of stochastic differential delay systems with impulsive jump and Markovian switching" by L. Gao gives a novel P-moment stability criteria for stochastic differential delay systems.  ...  Finally, the fundamental work of all reviewers on these papers is also very greatly acknowledged. Guangdeng Zong Wei Xing Zheng Ligang Wu Yang Yi  ... 
doi:10.1155/2013/198245 fatcat:yuymolnumvefbjba772h5wmuru
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