| CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS |
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| 引用本文： | 谢广明,王龙,叶庆凯.CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS[J].应用数学和力学(英文版),2003,24(9). |
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| 作者姓名： | 谢广明 王龙 叶庆凯 |
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| 作者单位： | Department of Mechanics and Engineering Science，Peking University，Department of Mechanics and Engineering Science，Peking University，Department of Mechanics and Engineering Science，Peking University Beijing 100871，P.R.China，Beijing 100871，P.R.China，Beijing 100871，P.R.China |
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| 基金项目： | theNationalNaturalScienceFoundationofChina(6992530760274001)，theNationalKeyBasicReasearchandDevelopmentProgram(2002CB312200)，thePostdoctoralProgramFoundationofChina |
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| 摘 要： | IntroductionHybriddynamicsystemscombinebothcontinuoustimedynamicsanddiscreteeventdynamics.Thetwodynamicsinteractoneachothersuchthatthesystemsperformmorecomplexdynamicbehaviors .Switchedlinearsystemsareanimportantclassofhybriddynamicsystemswhichconsistofafamilyoflineartime_invariantsystemsandaswitchinglawspecifyingtheswitchingbetweenthem .Inrecentyears ,therehasbeenincreasinginterestinthecontrolproblemsofswitchedsystemsduetotheirsignificancebothintheoryandapplications1～ 2 1] .Thusfar,therese…
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CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS ( Ⅰ )--BASIC PROPERTIES AND PRELIMINARY RESULTS |
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| XIE Guang_ming,WANG Long,YE Qing_kai.CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS ( Ⅰ )--BASIC PROPERTIES AND PRELIMINARY RESULTS[J].Applied Mathematics and Mechanics(English Edition),2003,24(9). |
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| Authors: | XIE Guang_ming WANG Long YE Qing_kai |
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| Abstract: | The controllability for switched linear system with time_delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time_delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis. |
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| Keywords: | hybrid dynamic system switched linear system time_delay controllability generalized cyclic invariant subspace switching sequence switching path |
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