·148· 工程科学学报，第38卷，第1期 (2):452 5结论 7]Liu B,Wang L,Sun D H,et al.Consensus of multiagent systems 本文研究了固定拓扑下由一阶和二阶智能体组成 with directed topology and communication time delay bases on the Laplace transform.Math Probl Eng,2014,2014:1 的混合离散系统在理想情况下和存在通信时延时的 [8]DjaidjaS,Wu Q H,Fang H.Leader-following consensus of doub- 致性问题，得到如下结论： le-integrator multi-agent systems with noisy measurements.Int J (1)提出的线性分布式一致性协议在一定条件下 Control Autom Syst,2015,13(1)17 可保证系统渐近一致： [9]Yin XX,Yue D,Hu S L.Consensus of fractional-order heteroge- (2)得到了系统实现一致的充分条件，该条件与 neous multi-ngent systems.IET Control Theory Appl,2013,7 协议控制参数、系统采样周期和拓扑结构有关； (2):314 [1o] (3)理想情况下系统的一致性平衡点依赖于系统 Zheng Y S,Zhu Y,Wang L.Consensus of heterogeneous multi- agent systems.IET Control Theory Appl,2011,5(16):1881 矩阵U的特征值1的左特征向量和系统的初始状态： [11]Zheng Y S,Wang L.Consensus of heterogencous multi-agent (4)系统的一致性不受有界通信时延影响. systems without velocity measurements.Int J Control,2012,85 (7):906 参考文献 [12]Liu C L,Liu F.Dynamical consensus seeking of heterogeneous [1]Tian Y P,Liu C L.Consensus of multi-agent systems with diverse multi-agent systems under input delays.Int J Commun Syst, input and communication delays.IEEE Trans Autom Control, 2013,26(10):1243 2008,53(9):2122 [13]Tian Y P,Zhang Y.High-order consensus of heterogeneous 2]Lin P,Jia Y M.Consensus of second-order discrete-time multi-- multi-agent systems with unknown communication delays. gent systems with nonuniform time-delays and dynamically chan- Automatica,2012,48(6):1205 ging topologies.Automatica,2009,45(9):2154 [14]Sun F L,Zhu W.Finite-ime consensus for heterogeneous multi- B]Liu C L.Liu F.Dynamical consensus seeking of second-order agent systems with mixed-order agents.Int J Syst Sci,2015,46 multi-agent systems based on delayed state compensation.Syst (11):1961 Control Let,2012,61(12):1235 [15]Zheng Y S,Wang L.Finite-time consensus of heterogeneous [4]Zhou W M,Xiao J W.Dynamic average consensus and consensus- multi-gent systems with and without velocity measurements.Syst ability of general linear multiagent systems with random packet Control Lett,2012,61(8):871 dropout.Abstr Appl Anal,2013,2013:1 [16]Ren W,Beard R W.Consensus seeking in multiagent systems [5]Ding L,Han Q L.Guo G.Network-ased leader-following con- under dynamically changing interaction topologies.IEEE Tranns sensus for distributed multi-agent systems.Automatica,2013,49 Automa Control,2005,50(5):655 (7):2281 07]Xiao F,Wang L.State consensus for multi-agent systems with [6]Zhou B,Lin Z L.Consensus of high-order multi-agent systems switching topologies and time-varying delays.Int J Control, with large input and communication delays.Automatica,2014,50 2006,79(10):1277工程科学学报，第 38 卷，第 1 期 5 结论 本文研究了固定拓扑下由一阶和二阶智能体组成 的混合离散系统在理想情况下和存在通信时延时的一 致性问题，得到如下结论: ( 1) 提出的线性分布式一致性协议在一定条件下 可保证系统渐近一致; ( 2) 得到了系统实现一致的充分条件，该条件与 协议控制参数、系统采样周期和拓扑结构有关; ( 3) 理想情况下系统的一致性平衡点依赖于系统 矩阵 U 的特征值 1 的左特征向量和系统的初始状态; ( 4) 系统的一致性不受有界通信时延影响． 参 考 文 献 ［1］ Tian Y P，Liu C L． Consensus of multi-agent systems with diverse input and communication delays． IEEE Trans Autom Control， 2008，53( 9) : 2122 ［2］ Lin P，Jia Y M． Consensus of second-order discrete-time multi-a￾gent systems with nonuniform time-delays and dynamically chan￾ging topologies． Automatica，2009，45( 9) : 2154 ［3］ Liu C L，Liu F． Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation． Syst Control Lett，2012，61( 12) : 1235 ［4］ Zhou W M，Xiao J W． Dynamic average consensus and consensus￾ability of general linear multiagent systems with random packet dropout． Abstr Appl Anal，2013，2013: 1 ［5］ Ding L，Han Q L，Guo G． Network-based leader-following con￾sensus for distributed multi-agent systems． Automatica，2013，49 ( 7) : 2281 ［6］ Zhou B，Lin Z L． Consensus of high-order multi-agent systems with large input and communication delays． Automatica，2014，50 ( 2) : 452 ［7］ Liu B，Wang L，Sun D H，et al． Consensus of multiagent systems with directed topology and communication time delay bases on the Laplace transform． Math Probl Eng，2014，2014: 1 ［8］ Djaidja S，Wu Q H，Fang H． Leader-following consensus of doub￾le-integrator multi-agent systems with noisy measurements． Int J Control Autom Syst，2015，13( 1) : 17 ［9］ Yin X X，Yue D，Hu S L． Consensus of fractional-order heteroge￾neous multi-agent systems． IET Control Theory Appl，2013，7 ( 2) : 314 ［10］ Zheng Y S，Zhu Y，Wang L． Consensus of heterogeneous multi￾agent systems． IET Control Theory Appl，2011，5( 16) : 1881 ［11］ Zheng Y S，Wang L． Consensus of heterogeneous multi-agent systems without velocity measurements． Int J Control，2012，85 ( 7) : 906 ［12］ Liu C L，Liu F． Dynamical consensus seeking of heterogeneous multi-agent systems under input delays． Int J Commun Syst， 2013，26( 10) : 1243 ［13］ Tian Y P，Zhang Y． High-order consensus of heterogeneous multi-agent systems with unknown communication delays． Automatica，2012，48( 6) : 1205 ［14］ Sun F L，Zhu W． Finite-time consensus for heterogeneous multi￾agent systems with mixed-order agents． Int J Syst Sci，2015，46 ( 11) : 1961 ［15］ Zheng Y S，Wang L． Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements． Syst Control Lett，2012，61( 8) : 871 ［16］ Ｒen W，Beard Ｒ W． Consensus seeking in multiagent systems under dynamically changing interaction topologies． IEEE Tranns Automa Control，2005，50( 5) : 655 ［17］ Xiao F，Wang L． State consensus for multi-agent systems with switching topologies and time-varying delays． Int J Control， 2006，79( 10) : 1277 · 841 ·