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Positivity and stability of timescale-type linear singular systems with time delays

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Science China(Information Sciences) 2022年第12期65卷 170-185页

作者： Xiaodong LU Haitao LI Xianfu ZHANG School of Mathematics and Statistics Shandong Normal University Key laboratory of systems and control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences School of control Science and Engineering Shandong University

This paper investigates positivity and stability problems of timescale-type delayed linear singular systems(LSSs). The existing results put an extremely strict constraint on the time-delay function. By introducing a novel function, this constraint is successfully removed, which generalizes the scope of the considered systems. Then, some necessary and sufficient criteria are proposed for the positivity of LSSs with bounded and infinite time-varying delays. Finally, the exponential(asymptotical) stability of LSSs with bounded(infinite) time-varying delays is analyzed. The derived results are also applicable to timescale-type differential-difference systems(DDSs). Compared with the existing stability criteria of DDSs with bounded time-varying delays, the strict limit on the parameter related to the convergence rate is eliminated. Hence,the conservatism of the existing results can be reduced. Moreover, when investigating stability of DDSs with infinite time-varying delays, this paper proposes a less conservative stability theorem. To illustrate the validity of the derived results, an example is presented regarding LSSs with bounded and infinite time-varying delays.

关键词： positivity stability time delay linear singular systems timescale-type systems

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Decay Rates of the Hyperbolic Equation in an Exterior Domain with Half-Linear and Nonlinear Boundary Dissipations

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Journal of systems Science & Complexity 2016年第3期29卷 657-680页

作者： LIU Yuxiang LI Jing YAO Pengfei Key laboratory of systems and control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences Shanxi University

This paper considers the energy decay of the wave equation with variable coefficients in an exterior *** damping is put on partly the boundary and partly on the interior of the *** energy decay results are established... 详细信息

关键词： Energy decay exterior domain hyperbolic equation Riemannian geometry method variable coefficients.

Symmetry-based decomposition of finite games

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Science China(Information Sciences) 2019年第1期62卷 164-176页

作者： Changxi LI Fenghua HE Ting LIU Daizhan CHENG School of Astronautics Harbin Institute of Technology Key laboratory of systems and control Academy of Mathematics and Systems SciencesChinese Academy of Sciences

The symmetry-based decompositions of finite games are investigated. First, the vector space of finite games is decomposed into a symmetric subspace and an orthogonal complement of the symmetric subspace. The bases of the symmetric subspace and those of its orthogonal complement are ***, the potential-based orthogonal decompositions of two-player symmetric/antisymmetric games are presented. The bases and dimensions of all dual decomposed subspaces are revealed. Finally, some properties of these decomposed subspaces are obtained.

关键词： potential game symmetric game decomposition Nash equilibrium semi-tensor product of matrices

Computational protein design and structure prediction—the 2024Nobel prize in chemistry

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Science China Chemistry 2025年

作者： Peilong Lu Lei Liu School of Life Sciences and Research Center for Industries of the Future Westlake University Tsinghua-Peking Joint Center for Life Sciences Ministry of Education Key Laboratory of Bioorganic Phosphorus Chemistry and Chemical Biology Center for Synthetic and Systems Biology Department of Chemistry Tsinghua University

The 2024 Nobel prize in chemistry recognizes groundbreaking advancements in protein science, highlighting the power of artificial intelligence (AI) to decipher and design the molecular machinery of life. Half of the prize was awarded to David Baker for the computational design of proteins; the other to Demis Hassabis and John Jumper for their AI-driven predictions of protein structures. This article briefly reviews their achievements, and discusses the opportunities and directions that their work has enabled (Figure1).

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Flocking with General Local Interaction and Large Population

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Journal of systems Science & Complexity 2019年第6期32卷 1498-1525页

作者： CHEN Ge LIU Zhixin Key laboratory of systems and control & National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper studies a flocking model in which the interaction between agents is described by a general local nonlinear function depending on the distance between agents. The existing analysis provided sufficient conditions for flocking under an assumption imposed on the system’s closed-loop states; however this assumption is hard to verify. To avoid this kind of assumption the authors introduce some new methods including large deviations theory and estimation of spectral radius of random geometric graphs. For uniformly and independently distributed initial states, the authors establish sufficient conditions and necessary conditions for flocking with large population. The results reveal that under some conditions, the critical interaction radius for flocking is almost the same as the critical radius for connectivity of the initial neighbor graph.

关键词： Consensus Cucker-Smale model flocking model multi-agent systems random geometric graph

STABILIZATION OF SWITCHED LINEAR systems WITH CONSTRAINED INPUTS

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Journal of systems Science & Complexity 2012年第1期25卷 60-70页

作者： Wei NI Daizhan CHENG Department of Mathematics School of ScienceNanchang University Key laboratory of systems and control Institute of Systems ScienceChinese Academy of Sciences

The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system＇s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.

关键词： Constrained inputs dwell time stabilization switched linear system.

Rock fracture mechanism of buffer blasting with cushion layer at the borehole bottom

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 325-334页

作者： Xinguang Zhu Chenxi Ding Zhe Sui Hong Su Xu Guo School of Civil and Resources Engineering University of Science and Technology BeijingBeijing 100083China Key laboratory for Mechanics in Fluid Solid Coupling systems Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of Mechanics and Civil Engineering China University of Mining and Technology(Beijing)Beijing 100083China School of Chemical and Blasting Engineering Anhui University of Science and TechnologyHuainan 232001China

This study primarily investigates the rock fracture mechanism of bottom cushion layer blasting and explores the effects of the bottom cushion layer on rock *** involves analyses of the evolution patterns of blasting stress,characteristics of crack distribution,and rock fracture features in the ***,blasting model experiments were carried out using the dynamic caustics principle to investigate the influence of bottom cushion layers and initiation methods on the integrity of the bottom rock *** experimental results indicate that the combined use of bottom cushion layers and inverse initiation effectively protects the integrity of the bottom rock ***,the process of stress wave propagation and dynamic crack propagation in rocks was simulated using the continuum-discontinuum element method(CDEM)and the Landau explosion source model,with varying thicknesses of bottom cushion *** numerical simulation results indicate that with increasing cushion thickness,the absorption of energy generated by the explosion becomes more pronounced,resulting in fewer cracks in the bottom rock *** illustrates the positive role of the cushion layer in protecting the integrity of the bottom rock mass.

关键词： bottom cushion layer blasting crack propagation continuum-discontinuum element method dynamic stress intensity factor

GENERAL DECAY RATE ESTIMATES FOR VISCOELASTIC WAVE EQUATION WITH VARIABLE COEFFICIENTS

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Journal of systems Science & Complexity 2014年第5期27卷 836-852页

作者： CAO Xiaomin YAO Pengfei School of Mathematical Sciences Shanxi University Key laboratory of control and systems Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.

关键词： Energy decay nonlinear boundary damping Riemannian metric viscoelastic wave equation

Map building for dynamic environments using grid vectors

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第7期12卷 574-588页

作者： Wen-fei WANG,Rong XIONG ,Jian CHU (State Key laboratory of Industrial control Technology,Institute of Cyber-systems and control,Zhejiang University,Hangzhou 310027,China) State Key laboratory of Industrial control Technology Institute of Cyber-Systems and Control Zhejiang University Hangzhou China

This paper addresses the problem of creating a geometric map with a mobile robot in a dynamic indoor *** form an accurate model of the environment,we present a novel map representation called the 'grid vector',which combines each vector that represents a directed line segment with a slender occupancy grid map.A modified expectation maximization (EM) based approach is proposed to evaluate the dynamic objects and simultaneously estimate the robot path and the map of the *** probability of each grid vector is evaluated in the expectation step and then used to distinguish the vector into static and dynamic *** robot path and map are estimated in the maximization step with a graph-based simultaneous localization and mapping (SLAM) *** representation we introduce provides advantages on making the SLAM method strictly statistic,reducing memory cost,identifying the dynamic objects,and improving the accuracy of the data *** SLAM algorithm we present is efficient in computation and *** on three different kinds of data sets show that our representation and algorithm can generate an accurate static map in a dynamic indoor environment.

关键词： Grid vector Line Segments Dynamic Simultaneous localization and mapping (SLAM) Expectation maximization (EM)