MINIMAL POLYNOMIAL MATRIX AND LINEAR MULTIVARIABLE SYSTEM(Ⅱ)

part(Ⅰ) of this work is on the theory of minimal polynomial matrix and Part(Ⅱ)is onthe applications of this theory to linear multivarible systeme.In I of this part,using the theory to Part(Ⅰ),some results about input part of a linearmultivarble system are discussed in detail and in Ⅱ,using duality properties,the conceptsabout row n.p.m.and row generating system,etc.are given. and some results about outputpart of linear multivariable system are discussed, too.In Ⅲ,we discuss the approach whichcan give the polynomial model with less dimension from the state-space model and in Ⅳ wediscuss tha inverse of the problem to give the state-space model from the polynomial model.Some interesting examples are given to explain the theory and the approach.     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ) —DISCRETE SYSTEMS AND BEAMS

IntroductionThestudiedobjectintheclassicstructuredynamicsisthepassivestructureswhicharechangedintoactivestructurewhencontroldevicesorsmartmaterialsareintroducedintoandthecontrolfunctionisapplied .Anactivestructureisgenerallycalledactivesystem .Asforthedefinitionofactivestructure ,itistheconceptofworthydiscussion[1].Thedefinitionshouldbebecomingrigorouswiththestudyontheactivestructuraldynamics.Withincertaincategoryofactivestructuresinpaper (Ⅰ ) [2 ],someattributesaboutthemodesoflinearactivest…     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅰ) —BASIC CONCEPTS AND PROPERTIES

IntroductionThestudyobjectoftheclassicstructuredynamicsispassivestructure .Whencontroldevicesorsmartmaterialareintroducedintoitwiththeapplicationofcontrolfunction ,thepassivestructuresarechangedintotheactivestructures.Theactivestructureisgenerallycalledactivesystem .Withtherapiddevelopmentofadaptivestructures,controlledstructuresandsmartstructures,therewillbemoreandmorekindsoftheactivestructures.Alotofspecialstudyontheactivestructureswillbedevelopedintooneofanewknowledgebranchinthefieldofthes…     

THE RELATIONSHIP BETWEEN THE STABILITY AND THE OPTIMALITY OF LINEAR SYSTEMS(Ⅱ)

Different from the inverse problem put forward by R.E.Kalman, another kind ofinverse problem of linear optimal control is proposed and discussed in[1] as follows:Givenan asymptotically stable linear constant system and a nonnegative quadratic performanceindex, when can a state-feedback be separated from the stable system so that this state-feedback control law is optimal for the given index? In this paper this problem is extended.Similar conclusions are obtained for linear discrete systems and linear time-variablesystems. According to these conclusions we can say that the correspondence between theasymptotically stable system and the optimal feedback system is the inherent character ofall kinds of linear systems.     

GEOMETRIC FRAMEWORK AND MINIMAL REALIZATIONS OF NONLINEAR SYSTEMS ON FIBRE BUNDLE

ＧＥＯＭＥＴＲＩＣＦＲＡＭＥＷＯＲＫＡＮＤＭＩＮＩＭＡＬＲＥＡＬＩＺＡＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳＯＮＦＩＢＲＥＢＵＮＤＬＥＭｕＸｉａｏｗｕ（慕小武）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓ...     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅱ ） — DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes ( Ⅰ ) “. The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS (Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZEDPERTURBED NLS SYSTEMS(Ⅰ)—POINCARÉ MAP

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅰ ） — BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.