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Robust Linear Neural Network for Constrained Quadratic Optimization

Zixin Liu, Yuanan Liu, Lianglin Xiong
2017 Discrete Dynamics in Nature and Society  
Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems.  ...  Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable.  ...  state trajectory of the designed dynamical system based on the numerical ordinary differential equation technique [11] .  ... 
doi:10.1155/2017/5073640 fatcat:hfsa7l67cbhr3cvifg2akavmjy

Page 2628 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
Lyapunov-Razumikhin type stability theorems.  ...  The authors introduce a new kind of positive definiteness of a Lyapunov function and prove Lyapunov-type theorems on stability and asymptotic stability of the zero solution of delay equations.  ... 

Page 6112 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
Then, based on them a Lyapunov-Razumikhin direct method is presented, which yields general direct criteria of practical stability.  ...  (RS-MIEM; Moscow) Stability of some functional-differential equations of retarded type.  ... 

On finite-time stabilization of a class of nonlinear time-delay systems: Implicit Lyapunov-Razumikhin approach

Artem N. Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor B. Furtat
2020 2020 59th IEEE Conference on Decision and Control (CDC)  
Theorems on Implicit Lyapunov-Razumikhin functions (ILRF) for asymptotic, exponential, finite-time and nearly fixed-time stability analysis of nonlinear time-delay systems are presented.  ...  Based on these results, finite-time stabilization of a special class of such systems is addressed.  ...  Razumikhin-type theorems Let us formulate a Lyapunov-Razumikhin theorem on asymptotic stability of time-delay systems [9] and its mild modifications [6] allowing one to estimate the exponential, finite-time  ... 
doi:10.1109/cdc42340.2020.9304421 fatcat:hms66esetzb4necpbgnkihuyp4

Moment exponential stability of random delay systems with two-time-scale Markovian switching

Fuke Wu, G. Yin, Le Yi Wang
2012 Nonlinear Analysis: Real world applications  
Using the limit system as a bridge, this paper establishes the Razumikhin-type criteria on the moment exponential stability.  ...  Dependence of stability on random time delays introduces technical difficulties beyond the existing literature.  ...  Razumikhin-type theorem of the random delay systems This section establishes a Razumikhin-type theorem on the pth moment exponential stability for the random delay system (2.3).  ... 
doi:10.1016/j.nonrwa.2012.02.013 fatcat:lfwsetlzkrejzjhjipl3zpspr4

Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching

Junhao Hu, Zhiying Xu
2014 Mathematical Problems in Engineering  
We develop exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching modeled by a continuous-time Markov chain which has a large state space.  ...  perturbed Lyapunov function methods and Razumikhin-type criteria.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/907982 fatcat:r2sctjpkm5btbgjzorgog5e66a

Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems [article]

Andreas Schlaginhaufen, Philippe Wenk, Andreas Krause, Florian Dörfler
2021 arXiv   pre-print
Based on classical time delay stability analysis, we then show how to ensure stability of the learned models, and theoretically analyze our approach.  ...  Learning how complex dynamical systems evolve over time is a key challenge in system identification.  ...  Based on classical time-delay stability theory, we then proposed a new regularization term based on a neural network Lyapunov-Razumikhin function to stabilize NDDEs.  ... 
arXiv:2110.14296v2 fatcat:rinbyaqpi5ccrju2hijkfgxaj4

Input-to-state stability analysis for interconnected difference equations with delay

Rob H. Gielen, Mircea Lazar, Andrew R. Teel
2012 MCSS. Mathematics of Control, Signals and Systems  
In practice, interconnections of dynamical systems, such as, for example, power systems, often show a geographical separation of the subsystems.  ...  Thus, a scalable ISS analysis method is obtained for large-scale interconnections of difference equations with delay.  ...  Gielen Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author  ... 
doi:10.1007/s00498-012-0080-4 fatcat:hx7naymprfg53hjs5qeh4zeqlu

A dither-free extremum-seeking control approach using 1st-order least-squares fits for gradient estimation

B.G.B. Hunnekens, M.A.M. Haring, N. van de Wouw, H. Nijmeijer
2014 53rd IEEE Conference on Decision and Control  
A stability proof is presented for the static-map setting which relies on a Lyapunov-Razumikhin type of proof for time-delay systems.  ...  Additionally, the absence of dither eliminates one of the time-scales of classical extremumseeking schemes, allowing for a possibly faster convergence.  ...  For the static-map setting a stability proof has been presented which relies on a Lyapunov-Razumikhin type of proof for time-delay systems.  ... 
doi:10.1109/cdc.2014.7039799 dblp:conf/cdc/HunnekensHWN14 fatcat:yvqjpbynhjhztcfmeaa2hxebxq

Small-gain results for discrete-time networks of systems with delay

Rob H. Gielen, Mircea Lazar, Andrew R. Teel
2011 IEEE Conference on Decision and Control and European Control Conference  
In this paper input-to-state stability for large-scale discrete-time networks of systems with delay is considered.  ...  In fact, as indicated in [9], the Razumikhin method is a type of small-gain approach that handles delays. Recently, based on  ...  ., [10] for the continuous-time case. IV. NETWORKS WITH LOCAL DELAYS Another cause for delay in networks of systems are inherent delays in the dynamical process in one or more of the systems.  ... 
doi:10.1109/cdc.2011.6160611 dblp:conf/cdc/GielenLT11 fatcat:vu2mdrbwe5aqxml5fxzhrrfdtu

Predictor-Based Remote Tracking Control of a Mobile Robot

Alejandro Alvarez-Aguirre, Nathan van de Wouw, Toshiki Oguchi, Henk Nijmeijer
2014 IEEE Transactions on Control Systems Technology  
A predictor-based control strategy capable of controlling the negative effects of the time-delay is proposed.  ...  Moreover, conditions are provided guaranteeing the local or global asymptotic stability of the closed-loop system up to a maximum admissible delay.  ...  Delay measurements presented in Section V validate this assumption on the delay, at least on time scales relevant to the (closed-loop) dynamics of the mobile robot.  ... 
doi:10.1109/tcst.2014.2304741 fatcat:4x5fe3cfuvbjjjl4at43apn2rq


Jun Liu, Xinzhi Liu, Wei-Chau Xie
2011 Journal of Nonlinear Science and its Applications  
Stability analysis is performed and stabilization strategies are proposed for a general class of stochastic delay differential equations subjected to switching and impulses.  ...  Both moment stability and almost sure stability of the resulting impulsive and switched hybrid stochastic delay systems are investigated using the well-known Lyapunov-Razumikhin method in the hybrid and  ...  Acknowledgements: The research for this work was supported by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.22436/jnsa.004.04.09 fatcat:cfmvrrunzbaxtarrp3b77jagmm

Delayed sliding mode control

Denis Efimov, Andrey Polyakov, Leonid Fridman, Wilfrid Perruquetti, Jean-Pierre Richard
2016 Automatica  
A timedelay modification/approximation of sign function is proposed, and it is shown that by substituting this new "sign" realization in the conventional sliding mode algorithms the main advantages of  ...  the sliding mode tools are preserved (like rejection of matched disturbances and hyper-exponential convergence 1 ), while the chattering is reduced.  ...  The problem of stability investigation in time-delay systems is much more complicated than for ordinary differential equations since design of a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin  ... 
doi:10.1016/j.automatica.2015.10.055 fatcat:zsmp2rsr3nevjajgwjd4ism45i

Razumikhin-Type Theorems on Exponential Stability of SDDEs Containing Singularly Perturbed Random Processes

Junhao Hu, Xuerong Mao, Chenggui Yuan
2013 Abstract and Applied Analysis  
This paper concerns Razumikhin-type theorems on exponential stability of stochastic differential delay equations with Markovian switching, where the modulating Markov chain involves small parameters.  ...  Under Razumikhin-type conditions, we establish theorems that if the limit systems are 𝑝th-moment exponentially stable; then, the original systems are 𝑝th-moment exponentially stable in an appropriate  ...  Acknowledgment This paper was supported by the National Science Foundation of China with Grant no. 60904005.  ... 
doi:10.1155/2013/854743 fatcat:7fqeaqhdevek3e65hj4ur5igtm

A note on continuous delayed sliding mode control

D. Efimov, A. Polyakov, L. Fridman, W. Perruquetti, J.-P. Richard
2015 2015 European Control Conference (ECC)  
the sliding mode tools are preserved (like time of convergence and uniformity of stability with respect to matched disturbances), while the chattering is seriously reduced.  ...  A timedelay modification/approximation of sign function is proposed, and it is shown that by substituting this new "sign" realization in the conventional sliding mode algorithms the main advantages of  ...  The dynamical systems subjected by a time-delay, whose models are described by functional differential equations, find their applications in different areas of science and technology [15] .  ... 
doi:10.1109/ecc.2015.7330897 dblp:conf/eucc/EfimovPFPR15a fatcat:hy6bzrxo55cvzbni7krngrq2xi
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