CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the oneperiodic, multiple-periodic controllability of periodic-type systems and controllability of periodic systems are presented, respectively. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Research and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972 ∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)｜i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1　Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME-DELAY CASE

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Research and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972≈), Doctor (E-mail:xiegming@mech.pku.edu.cn)     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

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. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Reasearch and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

IntroductionHybriddynamicsystemscombinebothcontinuoustimedynamicsanddiscreteeventdynamics.Thetwodynamicsinteractoneachothersuchthatthesystemsperformmorecomplexdynamicbehaviors .Switchedlinearsystemsareanimportantclassofhybriddynamicsystemswhichconsistofafamilyoflineartime_invariantsystemsandaswitchinglawspecifyingtheswitchingbetweenthem .Inrecentyears ,therehasbeenincreasinginterestinthecontrolproblemsofswitchedsystemsduetotheirsignificancebothintheoryandapplications[1～ 2 1] .Thusfar,therese…     

ADAPTIVE H-INFINITY CONTROL OF A CLASS OF UNCERTAIN NONLINEAR SYSTEMS

It is concerned with the problem of disturbance attenuation with stability for uncertain nonlinear systems by adaptive output feedback. By a partial-state observer and Backstepping technique, an adaptive output feedback controller was constructed, which can solve the standard gain disturbance attenuation problem with internal stability.     

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＯｗｉｎｇｔｏｔｈｅｆａｃｔｔｈａｔｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅＤｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｓｆｏｒａｃｌａｓｓｏｆｓｙｓｔｅｍｓｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｔｈｅｆｏｒｍｕ″=ｖ ,εｖ″ ｆ(ｘ ,ｕ ,ｕ′)ｖ′ -ｇ(ｘ ,ｕ ,ｕ′)ｖ=0　　 ( 0 <ｘ <1,0 <ε 1) ,ｕ( 0 ;ε) =0 ,ｕ( 1;ε) =0 ,ｖ( 0 ;ε) =α ,ｖ( 1;ε) =β,( 1)ｈａｖｅｔｈｅｑｕａｌｉｔａｔｉｖｅｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｏｆａｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｓｙｓｔｅ…     

A HYBRID GRANULARITY PARALLEL ALGORITHM FOR PRECISE INTEGRATION OF STRUCTURAL DYNAMIC RESPONSES

Precise integration methods to solve structural dynamic responses and the corre- sponding time integration formula are composed of two parts:the multiplication of an exponential matrix with a vector and the integration term.The second term can be solved by the series solu- tion.Two hybrid granularity parallel algorithms are designed,that is,the exponential matrix and the first term are computed by the fine-grained parallel algorithm and the second term is com- puted by the coarse-grained parallel algorithm.Numerical examples show that these two hybrid granularity parallel algorithms obtain higher speedup and parallel efficiency than two existing parallel algorithms.     

NUMERICAL METHOD IN DYNAMIC RESPONSE OF NONLINEAR SYSTEMS

A kind of modal synthesis techniques.which is applicable to vibration analysis forlinear substructures with nonlinear coupling attachments,has been extended to nonlineardynamic analysis of large complex structural systems.In this paper,a process issuggested to dynamic analysis of large complex structural systems with nonlinearcharacteristics of each substructure.At the end of this paper,an example showsthe defendable accuracy of the results and high efficiency of this process.     

ON SELF-EXCITED OSCILLATION OF DYNAMIC SYSTEMS WITH GAP

In this paper, the sufficient condition for self-excited oscillation of dynamic systems with gap is given by using qualitative method of differential equations.     

ROBUST CONTROL VIA STATE FEEDBACK FOR A CLASS OF UNCERTAIN BILINEAR SYSTEMS

ＲＯＢＵＳＴＣＯＮＴＲＯＬＶＩＡＳＴＡＴＥＦＥＥＤＢＡＣＫＦＯＲＡＣＬＡＳＳＯＦＵＮＣＥＲＴＡＩＮＢＩＬＩＮＥＡＲＳＹＳＴＥＭＳ￥ＣｈｅｎＳｏｎｇｌｉｎ（陈松林）；ＺｈｕＺｕｃｈｉ（朱祖慈）（ＥａｓｔＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＭｅｔａｌｌｕｒｇ...     

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｉｎｔｅｒｅｓｔｉｎｇｆｅａｔｕｒｅｉｎｔｈｅｆｒｅｅｖｉｂｒａｔｉｏｎｏｆａｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｉｓｔｈｅｆａｃｔｔｈａｔｔｈｅｎｕｍｂｅｒｏｆｅｘｉｓｔｉｎｇｎｏｒｍａｌｍｏｄｅｓｍａｙｅｘｃｅｅｄｔｈｅｎｕｍｂｅｒｏｆｄｅｇｒｅｅｓｏｆｆｒｅｅｄｏｍ ,ａｐｈｅｎｏｍｅｎｏｎｎｏｔｅｎｃｏｕｎｔｅｒｅｄｉｎａｌｉｎｅａｒｓｙｓｔｅｍａｎｄｃａｕｓｅｄｂｙｍｏｄｅｂｉｆｕｒｃａｔｉｏｎ .Ｔｈｅｒｅｆｏｒｅｍｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｏｎｅｏｎｔｈｅｓｔ…     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

The study of linear and global properties of linear dynamical systems on vector bundles appeared rather extensive already in the past. Presently we propose to study perturbations of this linear dynamics. The perturbed dynamical system which we shall consider is no longer linear, while the properties to be studied will be still global in general. Moreover, we are intersted in the nonuniformly hyperbolic properties. In this paper, we set an appropriate definition for such perturbations. Though it appears somewhat not quite usual, yet has deeper root in standard systems of differential equations in the theory of differentiable dynamical systems. The general problem is to see which property of the original given by the dynamical system is persistent when a perturbation takes place. The whole content of the paper is devoted to establishing a theorem of this sort.     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

ＮＯＴＥＳＯＮＡＳＴＵＤＹＯＦＶＥＣＴＯＲＢＵＮＤＬＥＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＳ（Ⅱ）──ＰＡＲＴ１ＬｉａｏＳｈａｎｔａｏ（廖山涛）Ａｂｓｔｒａｃｔ：Ｔｈｅｓｔｕｄｙｏｆｌｉｎｅａｒａｎｄｇｌｏｂａｌ．ｐｒｏｐｅｒｔｉｅｓｏｆｌｉｎｅａｒｄｙｎ...     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)──PART 2

IV.ChangingVariablesTheproofofthemaintheoremstatedinSectionIofthepaperwillbecompletedinSectionVI.Now,withthesystem.)giveninSectionill,letuswritesimplyTheexistenceofsuchf(k)followsfromtheproperty(II)ofthesystem.).Theexistenceisunique.Thenbytheproperty(II)o…     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)─PART 2

In the part 2, theorem 3.1 studied in part 1^[15] is proved first. The proof is obtained via a way of changing variables to reduce the original system of differential equations to a form concerning standard systems of equations in the theory of differentiable dynamical systems. Then by using theorem 3.1 together with the preliminary theorem 2.1, the main theorem of this paper announced in part 1 is proved. The definition of admissible perturbation is contained in the appendix of part 2. The meanings of the main theorem is described in the introduction of part 1.     

ON GRAMMATICAL COMPLEXITY OF A CLASS OF ATTRACTORS

ＯＮＧＲＡＭＭＡＴＩＣＡＬＣＯＭＰＬＥＸＩＴＹＯＦＡＣＬＡＳＳＯＦＡＴＴＲＡＣＴＯＲＳＬｕＱｉｎｈｅ（卢钦和）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔ｝＇．Ｓｕｚｈｏｕ２１５００６．Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔ...     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅰ)

ＮＯＴＥＳＯＮＡＳＴＵＤＹＯＦＶＥＣＴＯＲＢＵＮＤＬＥＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＳ（Ⅰ）ＬｉａｏＳｈａｎｔａｏ（廖山涛）（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔａｎｄＭａｔｈｅｍａｔｉｃｓＩｎｓｔｉｔｕｔｅ，ＰｅｋｉｎｇＵｎｉｒｅｒｓｉｔｙ，...     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅰ)

This paper is a continuation of a previous one. We still emphasize the discussion on the relation between the dynamics on the base space of a vector bundle and that on each associated bundle of frames.