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THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED one-sided Lipschitz condition

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Journal of Computational Mathematics 2023年第4期41卷 663-682页

作者： Yidan Geng Minghui Song Mingzhu Liu School of Mathematics Harbin Institute of TechnologyHarbin 150001China Digital Technology Research Center China Electronics Standardization InstituteBeijing100007China

In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.

关键词： Stochastic differential equations Piecewise continuous argument one-sided Lipschitz condition Truncated Euler-Maruyama method

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Global Practical Exponential Stabilization for one-sided lipschitz Systems with Time Delay

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Journal of Systems Science & Complexity 2022年第6期35卷 2029-2045页

作者： IMEN Akrouti NADHEM Echi Faculty of Sciences of Sfax Department of MathematicsSfax UniversityBP1171 Sfar 3000Tunisia Faculty of Sciences of Gafsa Department of MathematicsGafsa UniversityZarroug Gafsa 2112Tunisia

This paper addresses the practical stabilization problem for a class of one-sided lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the observer was confirmed.When external disturbances appear in the system,a separation principle is established,and the authors show that the closed loop system is exponentially practical stable.By choosing a suitable Lyapunov-Krasovskii functional,the authors derive new sufficient conditions to guarantee the exponential stability of the systems.Finally,a physical model is performed to prove the efficiency and applicability of the suggested approach.

关键词： Lyapunov-Krasovskii nonlinear time-delay systems one-sided Lipschitz condition separation principle

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Distributed H∞ filtering of nonlinear systems with random topology by an event-triggered protocol

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Science China(Information Sciences) 2021年第10期64卷 206-220页

作者： Yun CHEN Mengze ZHU Renquan LU Anke XUE Key Lab for IoT and Information Fusion Technology of Zhejiang Hangzhou Dianzi University School of Automation Guangdong University of Technology

Applying an event-triggered protocol, this paper proposes a distributed Hfilter design for nonlinear perturbed systems under fading measurements with random topology. Nonlinearities in this system obey the one-sided lipschitz constraint, which embraces the conventional lipschitz condition as a special case.The sensor network allows random variations of the interconnection strengths between adjacent nodes, and the connection coefficient is determined as the product of a constant and a stochastic variable with a known probabilistic feature. To reduce the unnecessary data transmission and efficiently use the limited bandwidth,the transmissions are orchestrated by an event-triggered regulating strategy. A stochastic bounded real lemma is established for the resulting error dynamics. Based on the presented matrix decomposition, which removes the direct coupling between the statistical information of interconnection strengths and the filter gain, the distributed Hfilter gain can be explicitly expressed and easily solved. The usefulness of the theoretical method is demonstrated in a simulation study.

关键词： sensor network distributed H ∞ filtering one-sided Lipschitz condition event-triggered protocol random topology

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