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New type of adaptive control for a class of distributed time-delay systems with adaptation regard to delay parameter

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Journal of Systems Engineering and Electronics 2010年第6期21卷 1054-1062页

作者： Lin Chai1, 2, Shumin Fei1, 2, Haiyan Jin1, 2, Ruimin Wang1, 2, and Yanhong Li1, 2 1. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Southeast University, Nanjing 210096, P. R. China 2. School of Automation, Southeast University, Nanjing 210096, P. R. China Key Laboratory of Measurement and Control of Complex Systems of Engineering Southeast University Nanjing 210096 P. R. China School of Automation Southeast University Nanjing 210096 P. R. China

The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is proposed for a memory proportional and integral （PI） feedback controller with adaptation to distributed time-delay. The feedback controller with memory simultaneously contains the current state and the past distributed information of the addressed systems. The design for adaptation law to distributed delay is very concise. The controller can be derived by solving a set of linear matrix inequalities （LMIs）. Two numerical examples are given to illustrate the effectiveness of the design method.

关键词： distributed delay linear matrix inequality （LMI） adaptive control time-delay systems memory PI feedback.

UNIFORM DECAY IN WEAKLY DISSIPATIVE TIMOSHENKO SYSTEM WITH INTERNAL distributed delay FEEDBACKS

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Acta Mathematica Scientia 2016年第3期36卷 815-830页

作者： Tijani A. APALARA Department of Mathematics University of Hafr AI-Batin (UoHB) Hafr AI-Batin 31991 Saudi Arabia

In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.

关键词： Timoshenko system well-posedness uniform stability distributed delay

Stochastic properties of solution for a chemostat model with a distributed delay and random disturbance

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International Journal of Biomathematics 2020年第7期13卷 205-229页

作者： Xiaofeng Zhang Rong Yuan Laboratory of Mathematics and Complex Systems(Ministry of Education)School of Mathematical Sciences Beijing Normal University Beijing 100875People’s Republic of China

In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.

关键词： Stochastic chemostat model distributed delay stochastic properties stochastically ultimate boundedness ergodicity

Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey

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International Journal of Biomathematics 2021年第4期14卷 85-120页

作者： Qun Liu Daqing Jiang Tasawar Hayat School of Mathematics and Statistics Key Laboratory of Applied Statistics of MOE Northeast Normal University Changchun 130024 Jilin ProvinceP.R.China College of Science China University of Petroleum Qingdao 266580Shandong ProvinceP.R.China Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group King A bdulaziz University JeddahSaudi Arabia

In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.

关键词： Stochastic predator-prey model stage structure distributed delay periodic solution positive recurrence

delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and distributed Time-varying delays

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International Journal of Automation and computing 2013年第1期10卷 18-31页

作者： P.Balasubramaniam T.Senthilkumar Department of Mathematics Gandhigram Rural University

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno （T-S） fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities （LMIs） and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

关键词： Robust stability robust H∞ control stochastic fuzzy systems distributed delay linear matrix inequality （LMI）

delay-DEPENDENT ROBUST STABILITY CRITERIA FOR UNCERTAIN SINGULAR NEUTRAL DIFFERENTIAL SYSTEMS WITH TIME-VARYING AND distributed delayS

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Annals of Differential Equations 2009年第2期25卷 150-160页

作者： Renji Han,Wei Jiang (School of Math. and Computation Science,Anhui University,Hefei 230039) School of Math. and Computation Science Anhui University Hefei 230039

The problem of delay-dependent robust stability for uncertain linear singular neutral systems with time-varying and distributed delays is investigated. The uncertainties under consideration are norm bounded,and possibly time varying. Some new stability criteria,which are simpler and less conservative than existing results,are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coeffcient matrix and formulated in...

关键词： uncertain singular neutral differential systems time-varying delay distributed delay Lyapunov-functional LMI asymptotic stability

Reduced-order H∞ filter design for singular neutral systems with distributed delay

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Reduced-order H∞ filter design for singular neutral systems...

Stability Analysis on Discrete-Time Cohen-Grossberg Neural Networks with Bounded distributed delay

第36届中国控制会议

作者： Guihua Li Yunxu Tong Shaodong Chen College of Mathematics and Statistics Nanyang Institute of Technology

The reduced-order H filtering problem for singular neutral systems with distributed delay is investigated in this paper. The Lyapunov stability theory and linear matrix inequality(LMI) approach are proposed to design a reduced-order H filter such that the filtering system remains asymptotically stable and the bound of H norm is less than a given level γ. Moreover, an explicit parametrization of all desired reduced-order filters is presented when these sufficient conditions are feasible. Finally, a numerical example is given to show the feasibility and effectiveness of the method.

关键词： Neutral systems Singular systems distributed delay Reduced-order H∞ filters

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Stability Analysis on Discrete-Time Cohen-Grossberg Neural N...

Synchronization of T-S Fuzzy Complex Dynamical Networks with Unknown Topological Structure and distributed Time-varying delay

第三十届中国控制会议

作者： LI Tao~(1,2),WANG Ting~2,and FEI Shumin~2 1.School of Electronic Engineering and Automation,Henan Polytechnic University,Jiaozuo 454000,Henan,P.R.China 2.Key Laboratory of Measurement and Control of Complex Systems of Engineering,Ministry of Education,Southeast University,Nanjing 210096,P.R.China

This paper investigates the asymptotical stability for discrete-time Cohen-Grossberg neural networks with both time-varying and distributed delays.By constructing a novel Lyapunov-Krasovskii functional and introducing some free-weighting matrices,one delay-dependent sufficient condition is obtained by using convex combination.The criterion is presented in terms of LMIs and the feasibility can be easily checked with the help of LMI in Matlab Toolbox.In addition,the activation function can be described more generally,which generalizes those earlier methods.Finally,the effectiveness of obtained results can be further illustrated by one numerical example in comparison with the existent ones.

关键词： Discrete-time Cohen-Grossberg neural networks（CGNNs） Asymptotical stability distributed delay LMI-based approach

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Synchronization of T-S Fuzzy Complex Dynamical Networks with...