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Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

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Journal of Systems Engineering and Electronics 2011年第5期22卷 799-809页

作者： Pei Cheng feiqi deng Yunjian Peng Systems Engineering Institute South China University of Technology Guangzhou 510640 P. R. China School of Mathematical Science Anhui University Hefei 230039 P. R. China

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.

关键词： impulsive stochastic systems time-varying delay exponential stability linear matrix inequality (LMI).

Coordination game model of co-opetition relationship on cluster supply chains

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Journal of Systems Engineering and Electronics 2008年第3期19卷 499-506页

作者： Zhou Min deng feiqi Wu Sai Inst. of Systems Engineering South China Univ. of Technology Guangzhou 510640 P. R. China School of Economic Management Guangdong Univ. of Technology Guangzhou 510520 P. R. China

The research of cluster supply chains is a new direction and a hotspot of the industrial cluster theory. On the condition of the coordination game, the enterprises may be stuck on the non-efficient equilibrium status, which becomes an important problem that must be considered on cluster supply chains. A symmetrical coordination game model is constituted to describe the competition and cooperation relationship of the same-quality manufacturers on cluster supply chains. The methods of the non-cooperation game theory and the evolutionary game theory are respectively used to analyze the model, whose parameters＇ influences under each method are then compared. It can be concluded that the analysis of the evolutionary game theory is more realistic and practical. Finally, three approaches are considered to break away from being path-dependence locked-in non-efficient status during this coordination game evolutionary process, which provide the development of cluster supply chains with an effective forecasting and Pareto optimizing method.

关键词： cluster supply chains coordination game non-cooperation game theory evolutionary game theory,path-dependence.

Study on stability in probability of general discrete-time stochastic systems

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Science China(Information Sciences) 2020年第5期63卷 215-217页

作者： Tianliang ZHANG feiqi deng Weihai ZHANG School of Automation Science and Engineering South China University of Technology College of Electrical Engineering and Automation Shandong University of Science and Technology

Dear editor,It is well-known that the stability should first be considered in system analysis and *** Lyapunov first initiated his stability theory regarding ordinary differential equations (ODEs)in 1892, Lyapunov’s stability theory has been an important research topic in both mathematics and control theory. Specifically, Lyapunov’s second method was soon generalized to the study of the stability of stochastic differential equa-

关键词： Study on stability in probability of general discrete-time stochastic systems

Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems

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Science China(Information Sciences) 2021年第10期64卷 5-20页

作者： Tianliang ZHANG feiqi deng Yuan SUN Peng SHI School of Automation Science and Engineering South China University of Technology School of Electrical and Electronic Engineering University of Adelaide

This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods,respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.

关键词： linear discrete stochastic systems fault estimation fault-tolerant control state transition matrix exponentialstability in mean square

Weighted average consensus problem in networks of agents with diverse time-delays

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Journal of Systems Engineering and Electronics 2014年第6期25卷 1056-1064页

作者： Wenhui Liu feiqi deng Jiarong Liang Xuekui Yan College of Automation Science and Engineering South China University of Technology School of Computer and Electronic Information Guangxi University

This paper studies the weighted average consensus problem for networks of agents with fixed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some sufficient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.

关键词： networks of agents distributed control weighted average consensus time-delay digraph theory

Input-to-state stability analysis of stochastic delayed switching systems

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Science China(Information Sciences) 2023年第11期66卷 204-221页

作者： Peilin YU feiqi deng Xueyan ZHAO Yuanyuan SUN School of Automation Science and Engineering South China University of Technology

In this paper, the issues regarding the input-to-state stability(ISS) and integral input-to-state stability(iISS) of the stochastic delayed switching systems with Lévy noise and input control(SDSS-LN-IC)are proposed by employing the comparison theorem approach, mode-dependent average dwell time(MDADT)method, delay integral inequality(DII), and Lyapunov-Razumikhin(L-R) technique. Two switching situations, namely, synchronous switching and asynchronous switching, are considered. Applying integral inequalities, sufficient stability conditions in both cases are given. Moreover, the sequences of this paper allow for the coefficients for the upper-bound expectation estimation of the infinitesimal operator to be mode-dependent,regardless of the sign and time-varying function rather than a constant, as is the case in certain existing results, which manifests the condition of the Lyapunov-Razumikhin technique in this paper is looser and less conservative. Finally, the validity and correctness of the theoretical results are verified by two examples and some simulations.

关键词： input-to-state stability synchronous switching asynchronous switching Lyapunov-Razumikhin technique mode-dependent average dwell time comparison theorem approach

Exponential stability of stochastic Markovian jump systems with time-varying and distributed delays

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Science China(Information Sciences) 2021年第10期64卷 251-253页

作者： Xueyan ZHAO feiqi deng Wenhua GAO School of Automation Science and Engineering South China University of Technology School of Mathematics South China University of Technology

Dear editor,In the field of applied mathematics and control theory,the research on stochastic Markovian jump systems has attracted increasing attention in recent years. A few studies have been conducted on stochastic Markovian jump systems [1–6]. Most previously conducted studies on stochastic Markovian jump systems investigate the discrete timevarying delay [4–6], whereas the distributed delay has not been given much attention owing to the difficulties involved in applying mathematical analysis.

关键词： stochastic Markovian jump systems Exponential stability distributed delays time-varying delays Lyapunov function

Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

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Science China(Information Sciences) 2018年第7期61卷 146-160页

作者： Haoyi MO Mengling LI feiqi deng Xuerong MAO School of Applied Mathematics Guangdong University of Technology Systems Engineering Institute South China University of Technology Department of Mathematics and Statistics University of Strathclyde

The exponential stability of trivial solution and numerical solution for neutral stochastic functional differential equations(NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory.

关键词： neutral stochastic functional differential equations with jumps almost sure exponential stability mean-square exponential stability Euler-Maruyama method

Stochastic stabilization using aperiodically sampled measurements

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Science China(Information Sciences) 2019年第9期62卷 91-101页

作者： Shixian LUO feiqi deng Xueyan ZHAO Zhipei HU School of Automation Science and Engineering South China University of Technology

This paper addresses the stabilization problem of sector-bounded nonlinear systems with sampled measurements via discrete-time stochastic feedback control. Unlike the previous studies, the closed-loop system is modeled as an impulsive stochastic differential equation. By developing a quasi-periodic polynomial Lyapunov function and sampling-time-dependent Lyapunov function based methods, two sufficient conditions for almost sure exponential stability are derived in terms of differential matrix inequalities(DMIs) and linear matrix inequalities(LMIs). It is shown that the DMI-based conditions can be formulated as a sum of squares(SOSs). Moreover, the obtained results are adapted to sampled-data stochastic/deterministic systems. The numerical examples illustrate the theoretical results.

关键词： stochastic stabilization almost sure stability sampled measurement discrete-time feedback control