minimum entropy control for discrete time time varying systems controllers that minimize a closed loop entropy criterion provide a means of trading off the robustness of h control with the performance of h2 optimal controllers a complete solution to the problem of finding a controller which minimizes the entropy of the closed loop input output operator for discrete time time varying systems is given the approach is based on a series of simpler problems a separation principle is also provided

a domain decomposition approach for full field measurements based identification of local elastic parameters abstract we propose a domain decomposition formalism specifically designed for the identification of local elastic parameters based on full field measurements this technique is made possible by a multi scale implementation of the constitutive compatibility method contrary to classical approaches the constitutive compatibility method resolves first some eigenmodes of the stress field over the structure rather than directly trying to recover the material properties a two steps micro macro reconstruction of the stress field is performed a dirichlet identification problem is solved first over every subdomain the macroscopic equilibrium is then ensured between the subdomains in a second step we apply the method to large linear elastic 2d identification problems to efficiently produce estimates of the material properties at a much lower computational cost than classical approaches

linked interpolation for reissner mindlin plate elements part ii a simple triangle the formulation and shape functions given in part i are extended to develop a simple plate bending triangle with good performance in both thin and thick situations indeed its performance is better than that of other nine dof elements and its computer implementation simpler when used with selective reduced integration the element produces identical results as that of xu 1 2 to save space details given in part i are not repeated and some results are also presented in the figures of part i

identification of symmetry type of linear elastic stiffness tensor in an arbitrarily orientated coordinate system abstract we develop a method through the mirror plane mp to identify the symmetry type of linear elastic stiffness tensor whose components are given with respect to an arbitrarily oriented coordinate system the method is based on the irreducible decomposition of high order tensor into a set of deviators and the multipole representation of a deviator into a scalar and a unit vector set since a unit vector depends on two euler angles we can illustrate the mp normals of the elastic tensor as zeros of a characteristic function on a unit disk and identify its symmetry immediately which is clearer and simpler than the methods proposed before furthermore by finding the common mps of three unit vector sets using fortran recipes we can also analytically recognize the symmetry type first and then recover the natural coordinate system associated with the linear elastic tensor the structures of linear elastic stiffness tensors of real materials with all possible anisotropies are investigated in detail

a new approach for analysis and synthesis of time varying systems in this paper new techniques are developed for the analysis of linear time varying ltv systems these lead to a formally simple treatment of robust control problems for ltv systems allowing methods more usually restricted to time invariant systems to be employed in the time varying case as an illustration of this methodology the so called h sub spl infin synthesis problem is solved for ltv systems

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

distance of a stiffness tetrad to the symmetry classes of linear elasticity abstract in the scope of linear anisotropic elasticity the fourth order elasticity tensor or tetrad has to be identified this can be done either by measurements or by numerical simulations an important task is then to identify a given tetrad probably with some experimental or numerical scattering with one of the symmetry classes for this purpose one needs a distance function between a given tetrad and the class of all tetrads with a particular symmetry which is zero if the tetrad obeys this symmetry or non zero otherwise in this paper we present a fast method to solve these problems we firstly introduce the 8th order projectors that map any stiffness tetrad into the part that is invariant under the action of a specific fixed symmetry group for this purpose we consider the seven out of the eight symmetry classes that are distinguishable in linear elasticity secondly since the symmetry axes of the specific stiffness tensor under consideration is generally not aligned with the used tensorial basis of the projector we need to rotate the sample stiffness the optimal orientation is obtained when the distance between the rotated stiffness and the rotated and projected stiffness is minimal thus we need to apply only linear mappings and minimize over three euler angles the latter is quite simple as the domain of the euler angles is periodic and the number of local minima is limited this procedure has the advantage that it is applicable in an algorithmic manner and does not require an a priori identification of symmetry planes symmetry axes or component symmetries which are only apparent under special choices for the tensorial basis

linked interpolation for reissner mindlin plate elements part i a simple quadrilateral in most plate elements using the reissner mindlin assumptions the interpolations used for the lateral displacements w and the rotation involve the independent representation of each variable by its nodal values usually with identical interpolations to ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element q4bl whose performance and robustness are good although it possesses one singularity if only three degrees of freedom are prescribed in part ii we apply the identical formulation to develop a triangular element t3bl which performs equally well and is fully robust

szego kac achiezer formulas in terms of realizations of the symbol abstract for rational and analytic matrix functions new formulas are obtained for the limits in the szego kac achiezer limit theorems in the rational case the new expressions are given in terms of finite matrices which come from special representations of the matrix functions these representations are known as realizations in mathematical systems theory

tradeoffs in linear time varying systems an analogue of bode s sensitivity integral bode s integral characterizes some of the tradeoffs imposed by the open loop dynamics of a linear time invariant system here we present an analogous time domain characterization applicable to time varying systems

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

determination of the symmetries of an experimentally determined stiffness tensor application to acoustic measurements abstract for most materials the symmetry group is known a priori and deduced from the realization process this allows many simplifications for the measurements of the stiffness tensor we deal here with the case where the symmetry is a priori unknown as for biological or geological materials or when the process makes the material symmetry axis uncertain some composites monocrystals the measurements are then more complicated and the raw stiffness tensor obtained does not exhibit any symmetry in the voigt s matrical form as it is expressed in the arbitrarily chosen specimen s base a complete ultrasonic measurement of this stiffness tensor from redundant measurements is proposed in a second time we show how to make a plane symmetry pole figure able to give visual information about the quasi symmetries of a raw stiffness tensor determined by any measurement method finally we introduce the concept of distance from a raw stiffness tensor to one of the eight symmetry classes available for a stiffness tensor the method provides the nearest tensor to the raw stiffness tensor possessing a chosen symmetry class with its associated natural symmetry base

elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material the issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed the optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry the solution is shown to be identical to minimizing a euclidean distance function or equivalently projecting the tensor of elastic stiffness onto the appropriate symmetry this has implications for how to best select anisotropic constants to acoustically model complex materials

logarithmic integrals and system dynamics an analogue of bode s sensitivity integral for continuous time time varying systems a new time domain interpretation of bode s integral is presented this allows for a generalization to the class of time varying systems which possess an exponential dichotomy it is shown that the sensitivity function is constrained on average by the spectral values in the dichotomy spectrum of the antistable component of the open loop dynamics

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

elasticity and symmetry of triangular lattice materials the elastic tensor of any triangular 2d lattice material is given with re spect to the geometry and the mechanical properties of the links between the nodes the links can bear central forces tensional material for example with hinged joints momentums flexural materials or a combination of the two the symmetry class of the stiffness tensor is detailed in any case by using the invariants of forte and vianello a distinction is made between the trivial cases where the elasticity symmetry group corresponds to the mi crostructure s symmetry group and the non trivial cases in the opposite case interesting examples of isotropic auxetic materials with negative poisson s ratio and non trivial materials with isotropic elasticity but anisotropic frac turation weak direction are shown the proposed set of equations can be used in a engineering process to create a 2d triangular lattice material of the desired elasticity

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

a transfer function approach to linear time varying discrete time systems in the first part of the paper a transfer function approach is developed for the class of linear time varying discrete time systems the theory is specified in terms of skew noncommutative rings of polynomials and formal power series both with coefficients in a ring of time functions the transfer function matrix is defined to be a matrix whose entries belong to a skew ring of formal power series it is shown that various system properties such as asymptotic stability can be characterized in terms of the skew ring framework in the last part of the paper the transfer function framework is applied to the study of feedback control new results are obtained on assignability of system dynamics by using dynamic output feedback and dynamic state feedback the results are applied to the control of an armature controlled do motor with a variable loading

the relationship between minimum entropy control and risk sensitive control for time varying systems the connection between minimum entropy control and risk sensitive control for linear time varying systems is investigated for time invariant systems the entropy functional and the linear exponential quadratic gaussian cost are the same in this paper it is shown that this is not true for general time varying systems it does hold however when the system admits a state space representation

linked interpolation for reissner mindlin plate elements part iii an alternative quadrilateral an alternative quadrilateral element for reissner mindlin plates which extends the mixed formulation described in part 1 using linked interpolations is presented differently from element q4bl presented in part i this element q4bla employs four internal rotation nodes and a linear approximation for transverse shear forces it is shown that the element passes various patch tests it does not possess any zero energy mode and its performance is good for both thick and thin plates

a triangular element based on reissner mindlin plate theory a new triangular plate blending element based on the reissner mindlin theory is developed through a mixed formulation emanating from the hu washizu variational principle a main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges