Full-Text Search：

Study on stability of hybrid systems composed of differential-algebraic subsystems

YAN Gang-feng, TONG Qing-yi, ZHAO Guang-zhou(College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China)
For the actuality that Differential-Algebraic Hybrid System (DAHS), whose subsystem is modeled by differential-algebraic equations, are seldom focused on by researchers at present but are important to direct the correlative research, a framework of stability theory including the definition of stability and (globally) asymptotic stability was put forward based on the model of DAHS. And the sufficient conditions to test for stability and asymptotic stability were achieved in the case of arbitrary switching and slow switching by Single Lyapunov Function (SLF) and Multiple Lyapunov Functions (MLF). For DAHS composed of only linear differential-algebraic subsystems, the switching law was presented to stabilize the whole system globally. The simulation results of a numerical example, in which the hybrid system composes of two linear differential-algebraic subsystems,are also investigated to show the feasibility and the effectiveness of the switching law. Analysis of power system showed that its voltage stability has the typical characteristics of hybrid system. However, the power subsystems cannot be described by pure Ordinary Differential Equation (ODE) but by Differential Algebraic Equation (DAE). Therefore, voltage stability boils down to the stability problem of Differential Algebraic Hybrid System (DAHS). In this paper, the power system model was used to degine the general form of DAHS ,then the stability theory framework was presented for the first time. The results of stable and asymptotically stable voltage were educed using Lyapunov's direct method. In the end, the simulation results showed that the stability theory results presented in this paper, can be successfully used for analysis of voltage stability. Then a novel tool is presented for research of voltage stability. The subsystem of hybrid system was modeled by differential-algebraic equations and pure differential equations. This class of hybrid systems, which was defined as differential-algebraic hybrid system (DAHS), was seldom researched at present. A framework of stability theory including the definition of stability and (globally) asymptotic stability was put forward based on the model of DAHS. And the sufficient conditions to test for stability and asymptotic stability were achieved in the case of arbitrary switching and slow switching by Single Lyapunov Function (SLF) and Multiple Lyapunov Functions (MLF). For DAHS composed of only linear differential-algebraic subsystems, the switching law governing the stability of the whole system globally was presented. The simulation results of a numerical example, in which the hybrid system composed of two linear differential-algebraic subsystems, were also investigated to show the feasibility and the effectiveness of the switching law.
【CateGory Index】： TP11
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
 【References】
 Chinese Journal Full-text Database 1 Hits
 1 LIU Kai,PENG Zhi-wei,HUANG Zhong,SUN Jin-chao(School of Electrical Engineering,Guizhou University,Guiyang 550003,China);Research on hybrid power system and its voltage stability based on mixed logic dynamic model[J];Relay;2008-10
 【Citations】
 Chinese Journal Full-text Database 3 Hits
 1 Tong Qingyi Yan Gangfeng (College of Electrical Engineering,Zhejiang University, Hangzhou, 310027);HYBRID SYSTEM AND ITS APPLICATION IN POWER SYSTEMS[J];Proceedings of The Csu-epsa;2003-02 2 ZHAO Hong-shan, Ml Zeng-qiang, REN Hui, YANG Qi-xun(Department of Electrical Engineering, North China Electric Power University, Baoding071003, China);Model and analysis of hybrid power systems with OLTC[J];Journal of North China Electric Power University;2003-02 3 ZHAO Hong-shan, MI Zeng-qiang, NIU Dong-xiao, YANG Qi-xun (North China Electric Power University, Baoding 071003, China);POWER SYSTEM MODELLING USING HYBRID SYSTEM THEORY[J];Proceedings of the Csee;2003-01
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 ZHANG Qun Li 1,DONG Xiu juan 2(1.Mathematics Dept.of Heze University,Heze 274015,China;2.Heze Advanced Skilled Workers' School,274026,China);Stability of a Class of RDDE[J];Journal of Anqing Teachers College(Natural Science Edition);2006-01 2 DING Gui-yan,HE Xi-qin (School of Science,University of Science and Technology Liaoning,Anshan 114051,China);Overview of research on monotone control systems[J];Journal of University of Science and Technology Liaoning;2008-01 3 ZHAO Li chun (Department of Mathematics,Anshan Normal University,Anshan Liaoning 114005,China);The robust persistence of lotka-volterra interval system[J];Journal of Anshan Normal University;2003-06 4 Jiang Fenghua (department of applied math in Nanjing Financial and Economic University 210003);The Criterion on the Stability of Exponent "Lipschitz'in the Universal Differential Equation of Function[J];Journal of Baicheng Teachers College;2004-04 5 YI Yu-yin(School of Management,Jinan University,Guangzhou 510632,China);Evolutionary Stability Analysis of Opportunistic Behavior[J];Journal of Chongqing University(Social Science Edition);2006-01 6 HU Jin(School of Science,Chongqing Jiaotong University,Chongqing 400074,China);The exponential stability of stochastic recurrent neural network with time delay[J];Journal of Chongqing Jiaotong University;2006-S1 7 SONG Qiankun (Dept.of Mathematics,Huzhou Teachers College,Huzhou Zhejiang 313000,China);Exponential Stability Criteria of Time-varying Interval Lurie Control Systems with Multi-delay[J];Journal of Chongqing Teachers College(Natural Science Edition);2003-01 8 SONG Qiankun(Dept.of Mathematics,Huzhou Teachers College,Huzhou Zhejiang 313000,China);Sufficient Criteria for the Stability of Time-varying Interval Matrices[J];Journal of Chongqing Teachers College(Natural Science Edition);2003-03 9 DONG Biao;WU Wen-quan;JIANG Zi-guo;PU Zhi-lin 1.Dept.of Mathematics,Aba Teachers College,Wenchuan Siehuan 623000;2.College of Mathematics and Software Science,Siehuan Normal University,Chengdu 610066,China;Global Exponential Stability of Bidirectionall Associate Memory in Neural Networks[J];Journal of Chongqing Nornal University(Natural Science Edition);2007-02 10 DONG Biao1,PU Zhi-lin2(1.Aba Teacher's Collge,Wenchuan Sichuan 623000;2.Collge of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China);Global Exponential Stability in Variably Delayed Hopfield Neural Network Models[J];Journal of Chongqing Normal University(Natural Science);2009-01
 【Co-references】
 Chinese Journal Full-text Database 10 Hits
 1 CHEN Yang-zhou, ZHANG Li-guo, CUI Ping-yuan ( College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100022, China );Stabilization of Linear Time-invariant (LTI) Planar Switched Systems[J];Journal of Beijing Polytechnic University;2004-02 2 EN Yang-zhou, LIN Lin, CUI Ping-yuan ( College of Electronic Information and Control Enginering, Beijing University of Technology, Beijing 100022, China );near-quadratic Optimal Control of Switched Hybrid System Based on Dynamic Programming Principle[J];Journal of Beijing Polytechnic University;2004-03 3 JIA Kun LI Hong-guang (College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China);Modeling of some food production processes based on hybrid Petri nets[J];Journal of Beijing University of Chemical Technology;2002-06 4 PENG Zhao,WANG Wen-hui, ZHOU Dong-hua(Dept.of Automatic,Tsinghua University, Beijing 100084, China);Multiple fault diagnosis of hybrid systems based on semi-qualitative method[J];Journal of Changchun Post and Telecommunication Institute;2004-04 5 ZHANG Xiao li, LIU Yu zhong, ZHAO Jun (School of Information Science & Engineering, Northeastern University, Shenyang 110006,China);Robust Control of a Class of Switched Systems[J];JOURNAL OF NORTHEASTERN UNIVERSITY;2000-05 6 LIU Yu zhong, ZHANG Xiao li, SUN Hong fei, ZHAO Jun (School of Information Science & Engineering, Northeastern University, Shenyang 110004,China);A Condition of Convex Combination for Quadratic Stability of Switched Nonlinear Systems[J];JOURNAL OF NORTHEASTERN UNIVERSITY;2001-06 7 ZHAO Jun, JIN Gang (School of Information Science & Engineering, Northeastern University, Shenyang 110004, China. Correspondent: ZHAO Jun, professor, E-mail: zdongbo@pub.ln.cninfo.net);Robust Fault-Tolerant Control for a Class of Uncertain Switched Nonlinear Systems[J];JOURNAL OF NORTHEASTERN UNIVERSITY;2004-03 8 SUN Wen-an, SUN Xi-ming, ZHAO Jun (School of Information Science & Engineering, Northeastern University, Shenyang 110004, China. );Asymptotic Stability of Linear Switched Systems with Polytopic Perturbations[J];JOURNAL OF NORTHEASTERN UNIVERSITY;2004-08 9 SUN Wen-an, SUN Xi-ming, ZHAO Jun(School of Information Science & Engineering, Northeastern University, Shenyang 110004, China.;Sufficient Condition for Quadratic Stability of Switched Linear Systems[J];JOURNAL OF NORTHEASTERN UNIVERSITY;2004-11 10 Hu Wei Lu Qiang (Tsinghua University Beijing 100084 China);Hybrid Power Control System and Its Application[J];Transactions of China Electrotechnical Society;2005-02
 【Secondary References】
 Chinese Journal Full-text Database 1 Hits
 1 LI Ji-fang1,2,TANG Tian-hao1,YAO Gang1(1.Logistics Engineering College,Shanghai Maritime University,Shanghai 200135,China; 2.Kaifeng University,Kaifeng 475004,China);Modeling and energy saving control for common DC bus AC drive system based on hybrid Petri nets[J];Power System Protection and Control;2011-06
 【Secondary Citations】
 Chinese Journal Full-text Database 10 Hits
 1 Qin Shiyin, Y. H. Song(l' Beijing Polytechnic University, Beijing 100022, China)(2. Brunei University, U. K. );THE ANALYSIS OF ARCHITECTURE OF HYBRID CONTROL SYSTEMS[J];AUTOMATION OF ELECTRIC POWER SYSTEMS;2000-11 2 L uShuqiang1 ,Qin Shiyin1 ,Y.H.Song2 1.Beijing Polytechnic U niversity,Beijing 10 0 0 2 2 ,China 2 .Brunel U niversity,U xbridge,Middlesex,U B83PH,U K;MODELLING AND SIMULATION OF EMERGENT FREQUENCY CONTROL FOR HYBRID POWER SYSTEMSBASED ON DIFFERENTIAL PETRI NETS[J];Automation of Electric Power Systems;2001-06 3 Zhang Yonggang, Ye Luqing(Huazhong University of Science and Techonlogy, 430074, Wuhan, China);CPN-BASED CONTROL OF OPERATING MODE TRANSITION FOR PUMPED-STORAGE SET Modeling And Imlementation[J];AUTOMATION OF ELECTRIC POWER SYSTEMS;1999-03 4 TONG Qing_yi, YAN Gang_feng (Zhejiang University , Hangzhou 310027,China);Voltage and reactive power control based on real-time database[J];Relay;2001-10 5 WU Jie and LIU Ming (Electric Power College, South China University of Technology · Guangzhou, 510640, P.R.China);Nonlinear Control and Its Applications in Power System[J];Control Theory & Applications;2002-01 6 Sun Jinxin Yang Cunbao Beijing Agricultural Engineering University;The Textured Model Method of VAR Comprehensive Optimization in Large Power Systems[J];Proceedings of the Csee;1991-03 7 Cai Zexiang Ni Yix inNortheast China Institute of Tsinghua UniversityElectrical Power Engineering;The Extended Equal Area Criterion (EEAC) Including Transient Stability Emergency Control[J];Proceedings of the Csee;1993-06 8 WANG Jie, CHEN Chen (Shanghai Jiaotong University,Shanghai 200030,China);NONLINEAR CONTROL OF DIFFERENTIAL ALGEBRAIC MODEL IN POWER SYSTEMS[J];Proceedings of the Csee;2001-08 9 Peng Zhiwei Hu Guogen Guizhou Institute of Technology,Guiyang,550003 China Han Zhenxiang Zhejiang University,Hangzhou,310027 China;DYNAMIC ANALYSIS OF THE POWER SYSTEM VOLTAGE STABILITY AFFECTED BY OLTC[J];Proceedings of the Csee;1999-02 10 Sun Yuanzhang ( Department of Electrical Engineering, Tsinghua University Beijing 100084);SYNTHESIS CONTROL THEORY AND PRACTICE OF STABILITY AND ECONOMIC IN POWER SYSTEMS[J];Bulletin of National Science Foundation of China;1999-03
Similar Journals
 > Computer Engineering and Design > Control Engineering of China > Journal of Shanghai Tiedao University(Natural Science Edition) > Control and Decision > Journal of South China University of Technology(Natural Science Edition) > Control Theory & Applications > Journal of Northeastern University(Natural Science) > Acta Automatica Sinica > Journal of Shanghai Jiaotong University > Journal of System Simulation