on undershoot and nonminimum phase zeros in this note we derive a simple necessary and sufficient condition for a stable system to exhibit an undershooting step response specifically we show that undershoot occurs if and only if the plant has an odd number of real right half plane zeros

perfect and subperfect regulation in linear multivariable control systems this paper is concerned with the synthesis of a high gain feedback control called perfect regulation p r for linear multivariable systems with external signals the existence condition for p r is derived in which the minimum phase property plays an essential role the use of an observer is discussed for achieving p r under restricted state observation some asymptotically ideal feedback properties are demonstrated such as the complete desensitization the complete servo performance with decoupling and the complete disturbance rejection which formulate the loop tightness for multivariable systems a design method for applying p r to non minimum phase systems called subperfect regulation s p r is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non minimum phase part it is a multivariable extension of a well known design technique for scalar systems to overcome the difficulty of phase non minimality computational procedures for p r and s p r are discussed an illustrative example is shown

optimal h sup infinity norm computation for multivariable systems with multiple zeros b c chang and j b peason s see ibid vol ac 29 p 880 7 oct 1984 computation of the optimal h sup infinity norm is generalized to the case with multiple right half plane zeros d sarason s 1967 interpolation theory is used to reduce the problem to a simple eigenvalue or singular value computation

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

computation of transmission zeros for distributed parameter systems the transmission zeros for a class of distributed parameter systems are defined as the limit points of the spectrum as the feedback gain increases to infinity a simple criterion which characterizes the transmission zeros different from the system operators spectrum is found the case when the transmission zeros belong to the spectrum is also discussed the presented theory is clarified with an example

on a convergent dsa preconditioned source iteration for a dgfem method for radiative transfer abstract we consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution the even parity equations are solved using a diffusion synthetic accelerated source iteration we provide a convergence analysis for the infinite dimensional iteration as well as for its discretized counterpart the diffusion correction is computed by a subspace correction which leads to a convergence behavior that is robust with respect to the discretization the proven theoretical contraction rate deteriorates for scattering dominated problems we show numerically that the preconditioned iteration is in practice robust in the diffusion limit moreover computations for the lattice problem indicate that the presented discretization does not suffer from the ray effect the theoretical methodology is presented for plane parallel geometries with isotropic scattering but the approach and proofs generalize to multi dimensional problems and more general scattering operators verbatim

characterization of all controlled invariant subspaces for spectral systems for a class of spectral systems a complete characterization of all controlled invariant subspaces contained in a closed subspace will be given this characterization is given in terms of the invariant zeros of the transfer function as a consequence of this we derive necessary and sufficient conditions for the existence of v operatorname ker c the largest controlled invariant subspace in the kernel of c

analysis of a full discretization scheme for 2d radiative conductive heat transfer systems abstract this paper deals with the convergence of numerical scheme for combined nonlinear radiation conduction heat transfer system in a gray absorbing and non scattering two dimensional medium the radiative transfer equation is solved using a discontinuous galerkin method with upwind fluxes the conductive equation is discretized using the finite element method moreover the crank nicolson scheme is applied for time discretization of the semi discrete nonlinear coupled system existence and uniqueness of the solution for the continuous and full discrete system are presented the convergence proof follows from the application of a discrete fixed point theorem involving only the temperature fields at each time step the order of approximation error stability and order of convergence are investigated finally the theoretical stability and convergence results are supported with numerical examples

computing the transmission zeros of large space structures the transmission zeros of a large space structure are frequently computed by means of the general purpose algorithm of a emami naeini and p van dooren 1982 it is shown that careful exploitation of the special form of the equations of motion of structural dynamics leads to an algorithm that is at least 60 times as fast as this when applied to an undamped structure and 15 times as fast for a lightly damped one

a note on the calculation and placing of finite zeros the finite zeros of a transfer function matrix are defined as the finite points on the complex plane to which the multivariable root loci converge as the loop gain increases infinitely in this paper an example is given where the finite zeros arc not obtained by the algorithm of kouvaritakis and macfarlane 1976 then a modification is suggested for the theorem which states a necessary and sufficient condition that the finite zeros are placed at stipulated n m points

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

chebyshev spectral sn method for the neutron transport equation we study convergence of a combined spectral and sn discrete ordinates approximation for a multidimensional steady state linear transport problem with isotropic scattering the procedure is based on expansion of the angular flux in a truncated series of chebyshev polynomials in spatial variables that results in the transformation of the multidimensional problems into a set of one dimensional problems the convergence of this approach is studied in the context of the discrete ordinates equations based on a special quadrature rule for the scattering integral the discrete ordinates and quadrature errors are expanded in truncated series of chebyshev polynomials of degree l and the convergence is derived assuming l s t 4 p s s where s t and s s are total and scattering cross sections respectively

finite element analysis of bifurcation in nonlocal strain softening solids progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise e g ill posedness and multiple bifurcation points this characteristics behavior favours spurious strain localization in numerical analyses and calls for the implementation of localization limiters for instance nonlocal damage constitutive relations the issue of possible stable or unstable equilibrium paths multiple localization zones and of the detection of bifurcation points has however never been addressed in the context of nonlocal constitutive laws we extend here the eigenmode analysis and perturbation method proposed by de borst to the study of the bifurcation and post bifurcation response of discrete nonlocal strain softening solids numerical applications on beams show that bifurcation and instability may occur in the post peak regime as opposed to the case of local constitutive relations the number of possible solutions at a bifurcation point is restricted due to the constraint introduced by the localization limiter and these solutions are shown to be mesh independent

analysis of a fully discrete scheme for neutron transport in two dimensional geometry we derive error estimates for a fully discrete scheme for the numerical solution of the neutron transport equation in two dimensional cartesian geometry obtained by using a special quadrature rule for the angular variable and the discontinuous galerkin finite element method with piecewise linear trial function for the space variable

choice of sampling to ensure minimum phase behaviour sufficient conditions for ensuring that a continuous stable proper minimum phase plant remains minimum phase when sampled have been derived as a corollary the critical sampling frequency the fastest sampling frequency ensuring minimum phase behaviour is shown to satisfy a simple equation an engineering method to obtain the critical sampling by use of a relay is proposed this method requires no prior knowledge of the plant

damage growth modeling using the thick level set tls approach efficient discretization for quasi static loadings the thick level set tls model is a damage model containing a non local treatment that prevents from spurious localization issues it also offers an automatic transition from damage to fracture the tls approach to model damage growth was first presented in moes et al 24 with a first numerical implementation for a time dependent damage evolution law in this paper we propose some improvements in terms of discretization and explicit damage growth algorithms to obtain a robust efficient and easy to implement model these improvements include a simple and efficient variational formulation for computing the non local quantities as well as the introduction of a so called ramped heaviside enrichment function to properly take into account the transition to cracks in fully damaged zones we consider here a simple explicit formulation for quasi static loadings decoupling the elastic computation and the damage growth the method is validated through standard benchmarks and compared to the griffith s fracture theory the convergence of energy and displacement errors is observed more complex computations including damage initiations are eventually performed

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

the transmission zeros of systems with delays in this paper we study the properties of the zeros of a system with general delays in the input state and control variables the main result of this paper shows that the zeros of the transfer function are always zeros of the system matrix with of at least the same multiplicity moreover when the system is canonical the zeros of the system matrix are zeros of the transfer function with the same multiplicity

determination of invariant zeros and zero directions of the system s a b c e mita 1977 presented a simple method for the invariant zeros of a linear multivariable system by constructing its maximal unobservable subspace mus however the results of this method have been restricted to a class of controllable and right invertible systems satisfying the diagonal decoupling condition and described by the triple a b c here a general method based on the theory of decoupling extends mita s results for all classes of systems described by the 4 tuples a b c e with no special requirements the mus of all classes of such systems is simply constructed and its order is given in terms of the system order n and the infinite zeros or the minimal observability indices of the system in addition the invariant zeros and zero directions are found from the eigenvalues and eigenvectors of a reduced order matrix having the dimension of the mus obtained directly from the state space parameters algorithms are presented for the invariant zeros and zero directions of invertible decouplable o

error estimation including pollution assessment for nonlinear finite element analysis a residual type error estimator for nonlinear finite element analysis is introduced this error estimator solves local problems avoiding both the computation of the flux jumps and the associated flux splitting procedure pollution errors are taken into account by a feedback strategy that is an error estimate based on local computations is used as the input of the pollution analysis this estimator is used in the frame of an adaptive procedure numerical examples show that the estimator is able to drive adaptive procedures leading to likely good solutions moreover one of the examples demonstrates that adaptive procedures are essential for complex highly nonlinear mechanical problems because they may discover secondary collapse mechanisms

the minimal delay decoupling problem feedback implementation with stability in this paper we solve the minimal delay decoupling problem of linear multivariable systems we look for feedback implementable solutions which moreover guarantee closed loop stability we prove that dynamic state feedback decoupling with stability is achievable if the number of independent inputs is large enough to compensate the intrinsic nondecouplability of the system we introduce new feedback invariants characterizing the minimal number of infinite and unstable zeros of the decoupled system

sampling infinite zeros and decoupling of linear systems abstract in order to understand more fully some of the trade offs involved in using a sampled data representation of a continuous time system the effects of time sampling on the ability to achieve disturbance decoupling and input output decoupling for linear systems are investigated it is shown that disturbance decouplability is lost through sampling whereas row by row dynamic input output decouplability is preserved in a very strong way these results are obtained by analyzing the structure at infinity of a sampled data system

non local damage model based on displacement averaging continuum damage models describe the changes of material stiffness and strength caused by the evolution of defects in the framework of continuum mechanics in many materials a fast evolution of defects leads to stress strain laws with softening which creates serious mathematical and numerical problems to regularize the model behaviour various generalized continuum theories have been proposed integral type non local damage models are often based on weighted spatial averaging of a strain like quantity this paper explores an alternative formulation with averaging of the displacement field damage is assumed to be driven by the symmetric gradient of the non local displacements it is demonstrated that an exact equivalence between strain and displacement averaging can be achieved only in an unbounded medium around physical boundaries of the analysed body both formulations differ and the non local displacement model generates spurious damage in the boundary layers the paper shows that this undesirable effect can be suppressed by an appropriate adjustment of the non local weight function alternatively an implicit gradient formulation could be used issues of algorithmic implementation computational efficiency and smoothness of the resolved stress fields are discussed copyright 2005 john wiley sons ltd

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

error assessment and mesh adaptivity for regularized continuous failure models this paper deals with the adaptive finite element analysis of structural failure a gradient enhanced damage model has been chosen to simulate material degradation since this model is regularized in the post peak regime the finite element solution does not suffer from pathological mesh dependence and thus converges to an objective solution upon mesh refinement however the error analyses have shown that the error in the nonlocal equivalent strain field becomes dominant during the post peak loading stages the accuracy of the nonlocal equivalent strain field and the corresponding damage quantity also greatly influences the accuracy of the quantity of interest two error measures have been proposed the goal oriented error estimates have provided similar error distributions although some small differences have been found in the softening regime objective error estimates together with adaptive criteria have been used to perform automated h adaptivity during computation

a treatment of jw axis model matching transformation zeros in the optimal h sup 2 and h sup infinity control designs a model matching transformation mmt zero is defined as a rank deficiency condition which prevents an h sup 2 or h sup infinity optimal control problem from being transformed into an equivalent model matching problem by imposing saturation constraints and accounting for additive instrument noise in the sensor and actuator signals all mmt zeros can be eliminated

a finite element method for the neutron transport equation in an infinite cylindrical domain we study the spatial discretization in a fully discrete scheme for the numerical solution of a model problem for the neutron transport equation in an infinite cylindrical domain based on using an interpolation technique in the discontinuous galerkin finite element procedure we derive an almost optimal error estimate for the scalar flux in the l2 norm combining a duality argument applied to the above result together with the previous semidiscrete error estimates for the velocity discretizations we also obtain globally optimal error bounds for the critical eigenvalues

on the generalized nyquist stability criterion the purpose of this paper is to provide a self contained proof of the generalized nyquist stability criterion the frequency dependent eigenvalues of a square transfer function matrix g 8 are defined directly from a matrix fraction decomposition of g 8 and a discussion of the fixed modes and fixed gains is given the theory of algebraic functions and riemann surfaces is employed in the proof and a detailed consideration is given to these theoretical ideas from the point of view of the stability result the question of the relationship between the poles and zeros of an algebraic function in the complex variable sense and the poles and zeros in the smith mcmillan sense is carefully examined and a proof of the argument principle for a regular region on a riemann surface is given

paper self tuning control of nonminimum phase systems the instability that arises from the pole zero cancellation of elementary self tuners and most mrac algorithms has given rise to a misapprehension that nonminimum phase systems can pose insoluble problems with the application of adaptive control since most practical processes exhibit some form of nonminimum phase behaviour particularly when controlled digitally this appeared to restrict the usefulness of self tuning methods however during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials the paper describes the practical features that a self tuning controller must possess and discusses how plant dead time and excess continuous time poles can lead to discrete time nonminimum phase zeros the source of instability of elementary self tuners is analysed and various suggested approaches for overcoming this problem are reviewed these include the use of a generalized minimum variance cost function incorporating control weighting factorization methods which avoid cancellation of the offending zeros adaptive control based on state space linear quadratic gaussian lqg theory and explicit pole placement via solution of a diophantine or bezoutian equation gawthrop s hybrid controller which avoids those nonminimum phase zeros due to continuous time pole excess is briefly discussed a series of simulations in which a nonminimum phase plant is subjected to a pattern of set point changes is presented to show some of the features of the algorithms in applications the order of the process is unlikely to be known or indeed be finite the pole placement algorithm which is particularly effective in the known order case is shown to lack robustness to underspecified order the use of a large control weighting however restores stability to the generalized minimum variance controller the conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum phase processes

an exact characterization of linear systems with zeros everywhere in the complex plane in this note an exact characterization of autonomous linear multivariable systems with zeros everywhere in the complex plane is given in terms of the system matrices such systems are called degenerate an important consequence of this characterization is that nondegeneracy is equivalent to the concept of functional reproducibility introduced by brockett and mesarovic based on this equivalence a new test for nondegeneracy in terms of the functional reproducibility matrix is derived an example is included to show that controllability observability and output controllability are not sufficient to guarantee the nondegeneracy of a linear system

a posteriori error estimation for standard finite element analysis a new residual type estimator based on projections of the error on subspaces of locally supported functions is presented the estimator is defined by a standard element by element refinement first an approximation of the energy norm of the error is obtained solving local problems with homogeneous dirichlet boundary conditions a later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces this estimate is a lower bound of the measure of the actual error the estimator does not need to approximate local boundary conditions for the error equation therefore computation of flux jumps is not necessary moreover the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward the presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error as well as its usefulness in adaptive procedures

adaptive technique for discrete models of fracture abstract static discrete models are advantageously used for the simulation of fracture in quasibrittle heterogeneous materials in order to correctly capture strain localization during the fracture process it is often necessary to represent material heterogeneity in the model directly via its discrete geometry depending on the specimen size and the size of the heterogeneities these simulations are typically extremely computationally demanding the contribution aims to reduce this computational cost via the implementation of adaptivity in the construction of the discrete model geometry the simulation starts with coarse discretization which provides correct elastic behavior and is then adaptively refined during the simulation in regions that suffer high stresses that induce cracking and strain localization the technique is applied in deterministic and probabilistic simulations and demonstrated on several examples

efficient and reliable nonlocal damage models we present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models the two major numerical challenges the strongly nonlinear highly localized and parameter dependent structural response of quasi brittle materials and the interaction between non adjacent finite elements associated to nonlocality are addressed in detail efficiency is achieved with a suitable combination of load stepping control technique and nonlinear solver for equilibrium equations reliability of the numerical results is ensured by an h adaptive strategy based on error estimation we use a residual type error estimator for nonlinear fe analysis based on local computations which at the same time accounts for the nonlocality of the damage model the proposed approach is illustrated by means of three application examples the three point bending test the single edge notched beam test and the brazilian test

a unified approach to remeshing strategies for finite element h adaptivity in h adaptivity a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution several authors have introduced different remeshing strategies yielding very different results in this work these methods are included in a unified framework emphasizing the role of the underlying hypotheses moreover an objective tool to evaluate the accuracy of the resulting finite element solution is presented thus a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions the different remeshing strategies are compared with well known numerical examples

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

optimal design of non minimum phase control systems with large plant uncertainty abstract a given linear time invariant controlled plant with non minimum phase and or unstable transfer function is considered that has significant plant parameter uncertainty but the ranges of the uncertain parameters are known it is desired that in response to a deterministic input over the entire range of parameter uncertainty the system output should lie with specified bounds a practical optimal design procedure that has been presented in the authors previous work is extended to deal with this problem furthermore the design philosophy is modified so that the two degree of freedom system configuration can be simplified

design of precompensators via infinite zero structure for dynamic decoupling of linear invertible systems the problem of designing precompensators necessary for decoupling invertible systems having weak inherent coupling is considered a simple algorithm which is directly applicable to systems characterized by square proper transfer function matrices t s is proposed for such design in the proposed algorithm the concept row reducedness at infinity of t s is utilized as an alternative necessary and sufficient condition for the decouplability of t s in addition to the simple design procedure of the compensator the algorithm yields the infinite zero structure of both t s and the resulting compensated system

stress based nonlocal damage model abstract progressive microcracking in brittle or quasi brittle materials as described by damage models presents a softening behavior that in turn requires the use of regularization methods in order to maintain objective results such regularization methods which describe interactions between points provide some general properties including objectivity and the non alteration of a uniform field as well as drawbacks damage initiation free boundary a modification of the nonlocal integral regularization method that takes the stress state into account is proposed in this contribution the orientation and intensity of nonlocal interactions are modified in accordance with the stress state the fundamental framework of the original nonlocal method has been retained making it possible to maintain the method s advantages the modification is introduced through the weight function which in this modified version depends not only on the distance between two points as for the original model but also on the stress state at the remote point the efficiency of this novel approach is illustrated using several examples the proposed modification improves the numerical solution of problems observed in numerical simulations involving regularization techniques damage initiation and propagation in mode i as well as shear band formation are analyzed herein

computation of the zeros and zero directions of linear multivariable systems a new geometric method of calculating multivariable system zeros and zero directions is presented by considering a particular choice of state feedback control law this control law has been motivated by the study of variable structure systems in the sliding mode the cases of singular and non singular cb have been treated separately

convergence adaptive refinement and scaling in 1d peridynamics we introduce here adaptive refinement algorithms for the non local method peridynamics which was proposed in j mech phys solids 2000 48 175 209 as a reformulation of classical elasticity for discontinuities and long range forces we use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected we discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1d in the limit of the horizon going to zero continuous micromoduli lead to optimal rates of convergence independent of the grid used while discontinuous micromoduli produce optimal rates of convergence only for uniform grids examples for static and dynamic elasticity problems in 1d are shown the relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement for the same number of nodes copyright 2008 john wiley sons ltd

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

the poles and zeros of a linear time varying system abstract for linear time varying discrete time and continuous time systems a notion of poles and zeros is developed in terms of factorizations of operator polynomials with time varying coefficients in the discrete time case it is shown that the poles can be computed by solving a nonlinear recursion with time varying coefficients in the continuous time case the poles can be calculated by solving a nonlinear differential equation with time varying coefficients the theory is applied to the study of the zero input response and asymptotic stability it is shown that if a time varying analogue of the vandermonde matrix is invertible the zero input response can be decomposed into a sum of modes associated with the poles stability is then studied in terms of the components of the modal decomposition

on blocking zeros and strong stabilizability of linear multivariable systems abstract motivated by a crucial role blocking zeros play in deciphering the strong stabilizability of a given system a careful study of blocking zeros is undertaken here after developing certain properties of blocking zeros and based on the multiplicity structure of invariant zeros we identify what kind of invariant zeros are blocking zeros for controllable and observable systems an invariant zero is a blocking zero if and only if its geometric multiplicity is equal to the normal rank of the transfer function of the given system this result leads to delineation of the class of controllable and observable time invariant linear systems into two subclasses 1 simply siso systems whose normal rank is unity and 2 truly mimo systems whose normal rank is greater than unity in a simply siso system every invariant zero is a blocking zero and hence a simply siso system is not necessarily strongly stabilizable on the other hand a truly mimo system with distinct invariant zeros does not have any blocking zeros and hence is always strongly stabilizable also given any truly mimo system there always exists an arbitrarily small perturbation of its dynamic matrix such that the perturbed system has no blocking zeros and hence is strongly stabilizable in this sense one can say that a mimo system almost always has no blocking zeros and hence is almost always strongly stabilizable

decentralized determinantal assignment problem fixed and almost fixed modes and zeros the decentralized determinantal assignment problem ddap is defined as the unifying description for the study of pole and zero assignment problems under decentralized output state feedback dof dsf and decentralized squaring down dsd respectively ddap is reduced to a linear problem of zero assignment of polynomial combinants and a multilinear problem of restricted decomposability of multivectors the decentralization characteristic dc and the decentralized polynomial grassmann representative d s gr of ddap are defined the fixed zero polynomial of ddap is then determined as the zero polynomial of d s gr the canonical d s gr cd r s gr and the decentralized plucker matrix dpm of ddap are introduced and necessary conditions for arbitrary assignment of the non fixed zeros are given in terms of the dpm the family of strongly zero non assignable sna systems is defined and for such systems the notion of the fixed zero is extended to that of the almost fixed zero afz an

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

on zeros of time invariant multivariable linear systems containing input derivatives a method is developed to find input vectors which generate zero output vectors in linear control systems whose state equation contains any finite number of derivatives of the input vector a general matrix eigenvalue problem is derived that may be reduced to an ordinary one

inverse stable sampled low pass systems it is shown that for low pass systems the fractional order hold and the pulse amplitude modulation signal reconstruction methods produce an inverse stable sampled transfer function h z in some cases when zero order hold fails to do so therefore they may be desirable alternatives to the zero order hold reconstruction in certain control problems the problem of how well h z models the continuous g s is also discussed

error estimates for the combined spatial and angular approximations of the transport equation for slab geometry we study the convergence of the discrete ordinates method in the numerical solution of the transport equation for slab geometry in particular the combined effect of spatial and angular approximations is analyzed general conditions are given which guarantee the stability of the combined approximations error estimates are derived for both the scalar flux in the l p norm 1 leqq p leqq infty and for the approximate critical eigenvalues a comparison with numerical results indicates that the eigenvalue error estimates are optimal

vibrational feedback control zeros placement capabilities it is shown that in addition to closed loop pole placement vibrational feedback controllers lead in the sense specified below to a possibility of open loop zeros assignability on this basis the superior performance characteristics of continuous time periodic controllers discovered in 3 6 are explained

comments on on blocking zeros in linear multivariable systems with reply reference is made to a recently published correspondence by p g ferreira in which concern was expressed about the name blocking zeros given in a paper by r v patel see ibid vol ac 31 p 239 41 mar 1986 to a newly defined class of zeros for multivariable linear systems the commenter refers to a few remarks about some well known results by ferreira and objects to the lack of precision in the wording of two of these remarks counterexamples to these well known results are presented in replying the original author claims that example 1 is not a counterexample to his statement and objects to some lack of precision in martin s words

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

disturbance decoupling problems via dynamic output feedback this paper considers the disturbance decoupling problems with or without internal stability and pole placement via dynamic output feedback using polynomial and rational matrix techniques we show that in all three problems considered the central solvability condition can be expressed as a two sided matching problem a bxc where a b and c are the polynomial system matrices of certain natural subsystems of the system model and x is to be determined over various subrings of the rational functions this matching problem can in turn be reduced to certain appropriate zero cancellation conditions on the polynomial system matrices a b and c

l p and eigenvalue error estimates for the discrete ordinates methods for two dimensional neutron transport the convergence of the discrete ordinates method is studied for angular discretization of the neutron transport equation for a two dimensional model problem with the constant total cross section and isotropic scattering considering a symmetric set of quadrature points on the unit circle error estimates are derived for the scalar flux in l p norms for 1 leqq p leqq infty a postprocessing procedure giving improved l infty estimates is also analyzed finally error estimates are given for simple isolated eigenvalues of the solution operator

error estimation and adaptivity for nonlocal damage models abstract nonlocal damage models are typically used to model failure of quasi brittle materials due to brittleness the choice of a particular model or set of parameters can have a crucial influence on the structural response to assess this influence it is essential to keep finite element discretization errors under control if not the effect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint to ensure the quality of the fe solution an adaptive strategy based on error estimation is proposed here it is based on the combination of a residual type error estimator and quadrilateral h remeshing another important consequence of brittleness is that it leads to structural responses of the snap through or snap back type this requires the use of arc length control with a definition of the arc parameter that accounts for the localized nature of quasi brittle failure all these aspects are discussed for two particular nonlocal damage models mazars and modified von mises and for two tests the brazilian tensile splitting test and the single edge notched beam test for the latter test the capability of the mazars model to capture the curved crack pattern observed in experiments a topic of debate in the literature is confirmed

a comparison between the nam and related techniques with a recent method for the computation of zeros and zero directions the annihilators n m of the input and output maps b c respectively of the linear state space model s a b c led to the nam algorithm for the calculation of system zeros a recent paper proposed an alternative algorithm and the present paper undertakes a comparison between the two it is shown that the new approach resembles the nam algorithm and indeed in all but the general case the two approaches are shown to be conceptually identical in the general case the new method fails to identify the precise set of zeros and this obviates the need for a comparison an examination of the computational aspects however demonstrates the advantages of the nam algorithm in both the calculation of zeros and zero directions

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

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process