dynamics of infinite classical anharmonic crystals we consider an unbounded lattice and at each point of this lattice an anharmonic oscillator that interacts with its first neighborhoods via a pair potential v and is subjected to a restoring force of potential u we assume that u and v are even nonnegative polynomials of degree 2 sigma 1 and 2 sigma 2 we study the time evolution of this system with a control of the growth in time of the local energy and we give a nontrivial bound on the velocity of propagation of a perturbation this is an extension to the case sigma 1 2 sigma 2 1 of some already known results obtained for sigma 1 ge 2 sigma 2 1

dirichlet form approach to infinite dimensional wiener processes with singular interactions we construct infinite dimensional wiener processes with interactions by constructing specific quasi regular dirichlet forms our assumptions are very mild accordingly our results can be applied to singular interactions such as hard core potentials lennard jones type potentials and dyson s model we construct nonequilibrium dynamics

fiedler companion linearizations for rectangular matrix polynomials the development of new classes of linearizations of square matrix polynomials that generalize the classical first and second frobenius companion forms has attracted much attention in the last decade research in this area has two main goals finding linearizations that retain whatever structure the original polynomial might possess and improving properties that are essential for accurate numerical computation such as eigenvalue condition numbers and backward errors however all recent progress on linearizations has been restricted to square matrix polynomials since rectangular polynomials arise in many applications it is natural to investigate if the new classes of linearizations can be extended to rectangular polynomials in this paper the family of fiedler linearizations is extended from square to rectangular matrix polynomials and it is shown that minimal indices and bases of polynomials can be recovered from those of any linearization in this class via the same simple procedures developed previously for square polynomials fiedler linearizations are one of the most important classes of linearizations introduced in recent years but their generalization to rectangular polynomials is nontrivial and requires a completely different approach to the one used in the square case to the best of our knowledge this is the first class of new linearizations that has been generalized to rectangular polynomials

minimal structure in the block decoupling problem with stability abstract in this paper we consider the block decoupling problem with stability we characterize the minimal mcmillan degree achievable for the block decoupled system for this we introduce a new list of integers which are feedback invariant these integers are related in a simple way to the minimal number of unstable and infinite zeros of the block decoupled system

parametric instability of a leipholz column under periodic excitation in this paper the parametric instability of a leipholz column under four boundary conditions is examined the study of this prototypical model is intended to provide a basic understanding of the disc brake pad instability the distributed follower type axial load is assumed to be uniform and periodic instability regions are obtained and the existence of combination resonances of the sum and difference types is discussed for each set of boundary conditions it is found that the combination resonance of the sum type exists in all the cases of boundary conditions considered but the difference type exists only in the cases of clamped simply supported and clamped free boundary conditions the combination resonance is shown to be as important as the simple parametric resonance results when compared to a column under a periodic end load show that the instability characteristics of these two columns are considerably different the effect of a constant axial load is to shift the instability regions along the frequency axis

instability of parametric dynamic systems with non uniform damping abstract a unified way of looking at parametric and combination resonances in systems with periodic coefficients and different amounts of damping in the various modes of vibration is presented the stability boundaries of the coupled mathieu equations are determined by the harmonic balance method fourier series with periods 2t and t being assumed the basic characteristics of the solution are discussed and the method is applied to multiple degree of freedom dynamic systems the destabilizing effect on the combination resonances is obtained by the present method

some analysis methods for rotating systems with periodic coefficients two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed the use of floquet methods and the use of multiblade coordinate and harmonic balance methods the analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems previously announced in star as n82 23702

an approach to investigate the instability of the multiple degree of freedom parametric dynamic systems a new analytical approach to the investigation of the regions of instability of multiple degree of freedom parametric dynamic systems is presented upon assuming a solution as a product of a characteristic component and a vector which has a periodic component expanding this vector into a fourier series and substituting it into the governing equations of motion a system of homogeneous algebraic equations can be obtained by the harmonic balance method then the problem of the stability of the non trivial solutions results in an eigenvalue problem of a non symmetricmatrix numerical results are presented for an undamped and damped mathieu equation whose stability has been investigated by various methods of solution the method has been applied to multiple degree of freedom systems such as lateral bending torsional vibration of a thin beam under parametric excitation and the parametric instability of a column under periodically varying axial loads

time evolution of two dimensional systems with infinitely many particles mutually interacting via very singular forces we study the existence and uniqueness of the time evolution via the newton law of a two dimensional system of infinitely many particles with very singular mutual interactions it is an improvement of the result by fritz and dobrushin given in comm math phys 57 67 81 1977 for inverse power like singular interactions

on non equilibrium dynamics of multidimensional infinite particle systems in the translation invariant case it is shown that for a set of full measure with respect to any translation invariant probability distribution on the space of initial configurarations of classical particle systems on d with interaction given by a smooth superstable potential of finite range there is a solution to the newtonian equations of motion provided that the specific energy and the particle density of the initial configuration exist a s

classical and quantum modes of coupled mathieu equations we expand the solutions of linearly coupled mathieu equations in terms of infinite continued matrix inversions and use it to find the modes which diagonalize the dynamical problem this allows obtaining explicitly the floquet lyapunov transformation to coordinates in which the motion is that of decoupled linear oscillators we use this transformation to solve the heisenberg equations of the corresponding quantum mechanical problem and find the quantum wavefunctions for stable oscillations expressed in configuration space the obtained transformation and quantum solutions can be applied to more general linear systems with periodic coefficients coupled hill equations periodically driven parametric oscillators and to nonlinear systems as a starting point for convenient perturbative treatment of the nonlinearity

infinite frequency structure and a certain matrix laurent expansion abstract a method for determining the smith mcmillan form at infinity of a rational matrix is derived by considering the laurent expansion at infinity of the matrix this method is used to provide a new test for the absence of infinite zeros in a rational matrix and a new formula for calculating the highest degree among the largest minors of a polynomial matrix

directed structure at infinity for infinite dimensional systems in this article the structure at infinity of infinite dimensional linear time invariant systems with finite dimensional input and output spaces is discussed it is shown that a diagonal form describing behaviour near infinity can be found this diagonal form is a generalisation of the smith mcmillan form at infinity for rational matrices it is then used to simplify certain solvability conditions of a regulation problem examples on time delay and distributed parameter systems are given

a transfer matrix approach to feedback invariants of linear systems application to decoupling abstract the transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups these transformation groups include the classical state feedback state and input changes of coordinates then the solvability of numerous classical control problems e g decouplability disturbance rejection model following can be expressed directly in terms of these invariants in this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems these invariants turn out to be crucial in studying feedback decoupling problems the main tools for this study are factorization of transfer matrices over the p i d of proper rational functions when dealing with stability we factor transfer matrices over the p i d of proper rational stable functions we illustrate the use of these invariants by studying some decoupling problems

minimal delay fir delayed left inverses for systems with zero nonzero zeros abstract this paper considers finite time input reconstruction for discrete time linear time invariant systems in the case where the initial condition is unknown there are three main results first a specific construction of finite impulse response fir delayed left inverse with the minimal delay for systems with zero nonzero zeros is presented next it is shown that in the presence of an arbitrary unknown initial condition finite time input reconstruction is possible using a delayed left inverse h if and only if h is fir finally it is shown that a transfer function with full column normal rank has an fir delayed left inverse with the minimal delay if and only if the system has zero nonzero zeros

a double expansion method for the frequency response of finite length beams with periodic parameters abstract a double expansion method for the frequency response of finite length beams with periodic distribution parameters is proposed the vibration response of the beam with spatial periodic parameters under harmonic excitations is studied the frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non periodic functions the procedure of the double expansion method includes the following two main steps first the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the floquet bloch theorem and the period parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients second the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions and the linear differential equations are converted into algebraic equations according to the galerkin method the expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined the proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively the modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method the proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis numerical results on the frequency response of the finite length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics including the parameter excited modal resonance doubling peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude the results have the potential application to structural vibration control

feedback representation of precompensators application to decoupling linear multi input multi output plants in this paper we examine the problem of internally stabilizing and simultaneously diagonally decoupling a linear multivariable system by two parameter compensation based on our earlier results boussaid and guerin 1996 we prove that any given plant p of full row rank can be decoupled with stability by the considered configuration computation of the decoupling compensators follows by easy constructions the decoupling problem with a minimum number of unstable zeros in the decoupled system is also formulated and solved in the generic case

on conditions guaranteeing two polynomial matrices possess identical zero structures some sufficient conditions for two polynomial matrices to simultaneously possess identical finite and infinite zero structures are developed a special case of this problem that of obtaining conditions under which a polynomial matrix has no infinite zeros is also considered and certain connections with previous work are established

equilibrium fluctuations for interacting brownian particles we consider an infinitely extended system of brownian particles interacting by a pair force gradv their initial distribution is stationary and given by the gibbs measure associated with the potentialv with fugacityz we assume thatv is symmetric finite range three times continuously differentiable superstable and positive and that the fugacity is small in the sense that 0 z 0 28 eedq 1 e v q in addition a certain essential self adjointness property is assumed we prove then that the time dependent fluctuations in the density on a spatial scale of order 1 and on a time scale of order 2 converge as 0 to a gaussian field with covariance edqg q e 2 t f q withp the density and the compressibility

analysis and geometry on configuration spaces the gibbsian case using a natural riemannian geometry like structure on the configuration space over rd we prove that for a large class of potentials the corresponding canonical gibbs measures on 1 can be completely characterized by an integration by parts formula that is if is the gradient of the riemannian structure on one can define a corresponding divergence div such that the canonical gibbs measures are exactly those measures for which and div are dual operators onl2 one consequence is that for such the corresponding dirichlet forms e are defined in addition each of them is shown to be associated with a conservative diffusion process on with invariant measure the corresponding generators are extensions of the operator div the diffusions can be characterized in terms of a martingale problem and they can be considered as a brownian motion on perturbed by a singular drift another main result of this paper is the following if is a canonical gibbs measure then it is extreme or a pure phase if and only if the corresponding weak sobolev spacew1 2 on is irreducible as a consequence we prove that for extreme canonical gibbs measures the above mentioned diffusions are time ergodic in particular this holds for tempered grand canonical gibbs measures ruelle measures provided that the activity constant is small enough we also include a complete discussion of the free case i e 0 where the underlying space rdis even replaced by a riemannian manifoldx

a new notion of equivalence for discrete time ar representations we present a new equivalence transformation termed divisor equivalence that has the property of preserving both the finite and the infinite elementary divisor structures of a square non singular polynomial matrix this equivalence relation extends the known notion of strict equivalence which dealt only with matrix pencils to the general polynomial matrix case it is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto regressive representations

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

a note on the solution of regular pmds a new resolvent decomposition of a regular polynomial matrix is derived which is a refinement of the results given by gohberg et al and vardulakis based on this a complete solution of the regular polynomial matrix descriptions pmds is presented that reflects precisely the zero input response and the zero state response and takes into account the impulsive properties of the system an algorithm for the computation of this resolvent decomposition is provided

on the structure at infinity of a structured system abstract we develop a graph theoretic characterization of the generic structure at infinity of the transfer matrix of a structured system we show that the generic structure at infinity can be determined by means of algorithms from combinatorial optimization based on the max flow min cut theorem and on results concerning minimal cost flows as an application of the obtained characterization we propose a structural version of two well known disturbance decoupling problems and we derive graph theoretic necessary and sufficient conditions for the solvability of each of the two problems

some remarks on nonequilibrium dynamics of infinite particle systems classical mechanics of infinitely many particles in dimensions one and two is considered particles interacting by a superstable pair potential of finite range the group of motion generated by newton s equations is constructed in the space of locally finite configurations with a logarithmic order of energy fluctuations at infinity a core of the liouville operator is also described results of dobrushin and the author and of marchioro pellegrinotti pulvirenti are improved

construction of infinite dimensional interacting diffusion processes through dirichlet forms by the theory of quasi regular dirichletforms and the associated special standard processes the existence of symmetric diffusion processes taking values in the space of non negative integer valued radon measures on mbox boldmath r nu and having gibbs invariant measures associated with some given pair potentials is considered the existence of such diffusions can be shown for a wide class of potentials involving some singular ones also as a consequence of an application of stochastic calculus a representation for the diffusion by means of a stochastic differential equation is derived

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

equivalence transformations of rational matrices and applications the known theories of transformations between polynomial matrices are extended to the case of rational matrices specifically equivalence between rational matrices having possibly different dimensions is defined and this has the property of preserving the zero structure of rational matrices in the region c some implications of this new equivalence transformation for linear system theory are also provided

relations between strict equivalence invariants and structure at infinity of matrix pencils the structure at infinity of matrix pencils is investigated via their smith macmillan forms at infinity 1 relations between some strict equivalence invariants and pole zero structure at infinity are established

pole assignment in the regular row by row decoupling problem by applying the canonical decomposition of the right invertible system c a b obtained in wei cheng and wang 2010 in this paper we derive a general formula of all solutions to the regular row by row decoupling problem based on this formula we characterize all attainable transfer function matrices for the decoupling and pole assignment problem in general cases the results obtained in this paper extend those in the literature

on coprime rational function matrices abstract the concept of coprimeness of matrices with elements in a field of fractions is introduced we focus on the field of rational functions and define when two rational matrices are coprime with respect to different rings the definition of coprimeness at infinity of polynomial matrices is obtained as a particular case moreover the fact that coprimeness is a local property is proved and it is shown how coprimeness changes by performing mobius transformations

a fundamental notion of equivalence for linear multivariable systems a fundamental form of equivalence of polynomial matrix descriptions of linear multivariable systems is defined based on the existence of a bijective map between the finite and infinite solution sets of the differential equations describing the two systems the connection with the system matrix relationship of full system equivalence is established

infinite frequency structure preserving transformations for general polynomial system matrices a recent transformation proposed for polynomial matrices is extended to the systems theory case of general polynomial system matrices two such extensions are proposed depending on whether the system matrix or its normalized form is used the relationship between both these transformations is established and under them all finite and infinite frequency system zero and pole structure is shown to be invariant

nonequilibrium dynamics of infinite particle systems with infinite range interactions we discuss the existence and uniqueness of nonequilibrium dynamics of infinitely many particles interacting via superstable pair interactions in one and two dimensions the interaction is allowed to be of infinite range and singular at the origin under suitable regularity conditions on the interaction potential we show that if the potential decreases polynomially as the distance between interacting two particles increases then the tempered solution to the system of hamiltonian equations exists moreover if the potential satisfies further that either it has a subexponential decreasing rate or it is everywhere two times continuously differentiable then we show that the tempered solution is unique the results extend those of dobrushin and fritz obtained for finite range interactions

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

time evolution of an infinitely extended vlasov system with singular mutual interaction we study the time evolution of an infinitely extended system in the mean field approximation governed by the vlasov equation this system is confined in an unbounded cylinder by an external force singular on the border the mutual interaction is assumed singular at short distance as 1 r alpha with alpha 2 3 or alpha 1 in case of an external lorentz force and with a short range the initial density is assumed bounded differently from studies which assume initial data compact in space and or in velocities here we consider a system having infinite mass and an exponential bound on the velocities according to the maxwell boltzmann law

dynamics of infinitely many particles mutually interacting in three dimensions via a bounded superstable long range potential we show existence and uniqueness for the solutions to the newton equations relative to a system of infinitely many particles moving in the three dimensional space and mutually interacting via a bounded superstable long range potential the present paper complete an analogous result obtained for positive short range interaction

matrix pencil equivalents of a general 2 d polynomial matrix a two level algorithm which reduces a general 2 d polynomial matrix to an equivalent matrix pencil form is presented the exact nature of the equivalence transformation connecting the matrix with its associated pencil is established

infinite eigenvalue method for stability analyses of canonical linear systems with periodic coefficients this paper presents a technique that provides both necessary and sufficient conditions for stability of canonical linear differential equations with periodic coefficients and is well suited for numerical application existing methods of stability analyses not subject to small parameter restrictions such as the widely used floquet numerical integration method fnim and the infinite determinant methods provide necessary conditions but are impractical for providing sufficient conditions for this class of systems with multiple degrees of freedom furthermore the infinite determinant methods are restricted to only certain classes of linear periodic systems whereas the fnim is subject to numerical problems when dealing with canonical systems the method proposed in this paper referred to as the infinite eigenvalue method iem is based on floquet theory and the infinite determinant methods it is applicable to the general class of multiple degree of freedom linear canonical systems and is not subject to small parameter restrictions a brief review of floquet theory and the fnim is given the iem is then presented and applied to a spacecraft dynamics problem of current interest the fnim is applied to the same problem and the two methods are compared

decoupling and pole assignment of singular systems a frequency domain approach abstract a new approach to the row by row decoupling of singular systems via state feedback and regular input transformation is presented the proposed method is based on the matrix fraction description of the system and is an extension of the frequency domain method for strictly proper systems the solvability condition of the problem is readily obtained from the numerator matrix of a coprime and column reduced matrix fraction description of the given system pole placement and decoupling is also considered and the characterization of the fixed poles is given

a wavelet galerkin procedure to investigate time periodic systems transient vibration and stability analysis abstract a wavelet galerkin procedure is introduced in order to obtain transient and periodic solutions of multi degree of freedom d o f s dynamical systems with time periodic coefficients numerical comparisons achieved with a runge kutta method emphasize that the wavelet based procedure is reliable even in the case of problems involving both smooth or non smooth parametric excitations and a relatively large number of degrees of freedom the procedure is then applied to study the vibrations of some theoretical parametrically excited systems since problems of stability analysis of non linear systems are often reduced after linearization to problems involving linear differential systems with time varying coefficients the method is shown to be effective for the computation of the floquet exponents that characterize stable unstable parameters areas and consequently allows estimators for stability instability levels to be provided stability diagrams of some theoretical examples including a single degree of freedom mathieu oscillator and a two degree of freedom parametrically excited system illustrate the relevance of the method finally future studies are outlined for the extension of the wavelet method to the non linear case

matrix fractions and strict system equivalence unimodular equivalence ue is defined for matrix fraction decompositions mfds it is shown that if an mfd is regarded as a quadruple d s n s i then uni modular equivalence and fuhrmann strict system equivalence coincide it is thus established that ue for mfds and system similarity for state space representations are exact counterparts a brief discussion on extended unimodular equivalence eue of polynomial matrices is included and a short polynomial matrix proof that the invariant factors of the smith form are preserved under eue is given

infinite elementary divisors of a matrix polynomial and implications a new characterization of infinite poles and zeros in terms of a natural extension of the idea of infinite elementary divisors of a matrix pencil to matrix polynomials is developed it is used to show that two previous descriptions of infinite frequency structure are equivalent subsequently a polynomial matrix transformation which simultaneously preserves the finite and infinite zero structure is presented

fundamental equivalence of discrete time ar representations we examine the problem of equivalence of discrete time auto regressive representations dtarrs over a finite time interval two dtarrs are defined as fundamentally equivalent fe over a finite time interval 0 n if their solution spaces or behaviours are isomorphic we generalize the concept of strict equivalence se of matrix pencils to the case of general polynomial matrices and in turn we show that fe of dtarrs implies se of the underlying polynomial matrices

analysis and geometry on configuration spaces abstract in this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds namely configuration spaces more precisely a differential geometry is introduced on the configuration space x over a riemannian manifold x this geometry is non flat even if x r d it is obtained as a natural lifting of the riemannian structure on x in particular a corresponding gradient divergence div and laplace beltrami operator h div gamma are constructed the associated volume elements i e all measures on x w r t which and div gamma become dual operators on l 2 x are identified as exactly the mixed poisson measures with mean measure equal to a multiple of the volume element dx on x in particular all these measures obey an integration by parts formula w r t vector fields on x the corresponding dirichlet forms e on l 2 x are therefore defined each is shown to be associated with a diffusion process which is thus the brownian motion on x and which is sub sequently identified as the usual independent infinite particle process on x the associated heat semigroup t t t 0 is calculated explicitly it is also proved that the diffusion process when started with is time ergodic or equivalently e gamma is irreducible or equivalently t t t 0 is ergodic if and only if is poisson measure z dx with intensity z dx for some z 0 furthermore it is shown that the laplace beltrami operator h div gamma gamma on l 2 x z dx is unitary equivalent to the second quantization of the laplacian x on x on the corresponding fock space n 0 l 2 x z dx n as another direct consequence of our results we obtain a representation of the lie algebra of compactly supported vector fields on x on poisson space finally generalizations to the case where dx is replaced by an absolutely continuous measure and also to interacting particle systems on x are described in particular the case where the mixed poisson measures are replaced by gibbs measures of ruelle type on x

spectral structures of the generalized companion form and applications in this note we investigate the relationship between the finite and infinite frequency structure of a regular polynomial matrix and that of a particular linearization called the generalized companion matrix a special resolvent decomposition of the regular polynomial matrix is proposed which is based on the weierstrass canonical form of this generalized companion matrix and the solution of a regular polynomial matrix description pmd is thus formulated from this resolvent decomposition both the initial conditions of the pseudostate and the input are considered

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

diagonal decoupling of linear systems by static state feedback a solution is presented to the long standing open problem of linear systems theory diagonal decoupling by static state feedback the earliest known investigation of system decoupling dates back to 1934 a state space formulation of the problem appeared in 1964 and a solution for square and invertible systems followed in 1967 the case of right invertible systems however has withstood all past efforts to obtain a solution save for several special cases the present formulation avoids restrictive hypotheses concerning system and decoupling feedback the existence of a solution is shown to depend on the existence of three lists of integers conditioned solely by system invariants with respect to the permissible transformations

achieving diagonal interactor matrix for multivariable linear systems with uncertain parameters abstract the notion of interactor matrix or equivalently the hermite normal form is a generalization of relative degree to multivariable systems and is crucial in problems such as decoupling inverse dynamics and adaptive control in order for a system to be input output decoupled using static state feedback the existence of a diagonal interactor matrix must first be established for a multivariable linear system which does not have a diagonal interactor matrix dynamic precompensation or dynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system such precompensation often depends on the parameters of system and is thus difficult to implement with accuracy when the system is subject to parameter uncertainty in this paper we characterize a class of linear systems which can be precompensated to achieve a diagonal interactor matrix without the exact knowledge of the system parameters more precisely we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensated system has a diagonal interactor matrix these conditions are associated with the so called non generic singularity of certain matrix related to the system structure but independent of the system parameters the result of this paper is expected to be useful in robust and adaptive designs

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

some new properties of the right invertible system in control theory in this paper we deduce equivalent conditions of controllability stability and observability of a right invertible system c a b by applying the canonical decomposition of c a b obtained by wei et al wei m cheng x wang q 2010 a canonical decomposition of the right invertible system with applications siam journal on matrix analysis and applications 31 4 1958 1981 we also derive three equivalent sufficient solvability conditions of the non regular row by row decoupling problem which are generalization of necessary and sufficient conditions of the regular row by row decoupling problem

on matrix polynomials with the same finite and infinite elementary divisors abstract a criterion is presented that characterizes when two matrix polynomials of any size rank and degree have the same finite and infinite elementary divisors this characterization inherits a coprimeness condition of the extended unimodular equivalence defined by pugh and shelton 17 in the set of real or complex matrix polynomials satisfying the constraint that the difference between the number of rows and columns is constant this extended unimodular equivalence is first generalized to matrices of any size with elements in any principal ideal domain

on the computation of the jordan canonical form of regular matrix polynomials in this paper an algorithm for the computation of the jordan canonical form of regular matrix polynomials is proposed the new method contains rank conditions of suitably defined block toeplitz matrices and it does not require the computation of the jordan chains or the smith form the segre and weyr characteristics are also considered

an extension of wolovich s definition of equivalence of linear systems wolovich s classical definition of equivalence for linear systems 1974 is extended to the generalized study of linear systems it is shown that the resulting equivalence is an alternative characterization of the notion of full system equivalence underlying its fundamental role in the generalized study of linear systems

decoupling of structured systems by parameter independent precompensation and state feedback in this paper structured systems described by state space models are considered for these systems the entries of the state space model matrices are assumed to be either fixed zeros or free independent parameters we study the dynamic decoupling of structured linear systems it turns out that a large class of systems which is not state feedback decouplable can be made decouplable by the addition of a simple structured precompensator such a precompensator then has the property to be independent of the system parameters we give a necessary and sufficient condition for a structured system to be made feedback decouplable using a parameter independent precompensator furthermore we prove that when such a solution exists the precompensator can be chosen to be diagonal in this case the precompensator is constructed via a simple combinatorial algorithm our approach is based on a graph representation of the structured system all the results of this paper are related to some particular shortest sets of input output paths in the graph associated with the structured system

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

gradient dynamics of infinite point systems nonequilibrium gradient dynamics of d dimensional particle systems is investigated the interaction is given by a superstable pair potential of finite range solutions are constructed in the well defined set of locally finite configurations with a logarithmic order of energy fluctuations if the system is deterministic and d 2 then singular potentials are also allowed for stochastic models with a smooth interaction we need d 4 in order to develop some prerequisites for the theory of hydrodynamical fluctuations in equilibrium we investigate smoothness of the markov semigroup and describe some properties of its generator 0 introduction the purpose of this paper is to study existence and regularity properties of solutions to the following infinite system of stochastic differential equations consider a countable set s of d dimensional particles suspended in a fluid where the interaction is given by a pair potential u rgd 00 oo in a quasi microscopic description of such systems the effect of collisions with the particles of the fluid can be represented by uncorrelated stochastic forces and the soft resistance of the liquid medium reduces the order of the equations of motion from two to one see 13 23 and 24 for some further references configurations of these systems are countable subsets of rd such that any bounded domain contains a finite number of points only particles of a configuration will be identified by labelling points by elements of s thus a

dirichlet forms and dirichlet operators for infinite particle systems essential self adjointness we study the dirichlet forms and the associated dirichlet operators for gibbs measures on infinite particle configuration space the dirichlet forms are defined to be gradient type forms by introducing a measurable field of rigged hilbert spaces on the configuration space under mild conditions on the interaction including singular potentials we show that the pre dirichlet operator is symmetric and that the closure of the pre dirichlet form satisfies the markovian property when the interaction is three times differentiable and decreasing sub exponentially we show that the dirichlet operator is essentially self adjoint on a domain consisting of bounded smooth local functions