necessary and sufficient stability conditions for the case of dependent additive perturbations in this paper we examine the stability properties of linear multivariable feedback systems in the presence of structured additive perturbations characterized by dependencies occurring in the perturbation matrix such dependencies may take the form of dependent phases between elements of element by element bounded perturbations and or repeated blocks in block structured perturbations by using non diagonal and possibly complex transformation matrices it is shown how stability conditions that are both necessary and sufficient may be obtained for this class of perturbation

generalized l sub 2 synthesis introduces a general framework for control design which can be used to solve several open problems in robust and optimal control these include systems subject to independently norm bounded disturbances robust stability for systems subject to element by element bounded structured uncertainty certain classes of robust performance problems and systems subject to deterministic white noise disturbances this is achieved by combining concepts such as h infinity optimization linear matrix inequalities and integral quadratic constraints necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite dimensional linear matrix inequality

robustness analysis with full structured uncertainties this paper deals with problems involving full structured rather than block diagonal uncertainty i e uncertainty blocks where each sub block or element may be an independent uncertainty rearranging this problem into standard block diagonal form results in an explosion in the required computation and so a number of researchers have proposed more efficient bounds in particular those based on non similarity scaling for such problems here we show how to map such problems into reduced size standard problems the standard bounds applied to the reduced size problem are then shown to be at least as accurate and require the same computational effort as earlier techniques with the added bonus that the standard upper bound is convex moreover this new approach is applicable in a much more general setting allowing one to efficiently compute both robust stability and robust performance for problems involving multiple real and complex uncertainty blocks any number of which may be full structured

dynamic performance interaction and the characteristic locus method a quantitative approach the characteristic locus method in addition to its role in the assessment of system stability is also an effective approach for evaluating tracking accuracy interaction and dynamic static loop performance however with regard to the evaluation of the latter three there exists a degree of ambiguity and personal judgement in addition to a requirement for a priori assumptions about proper problem conditioning this paper stipulates quantitative bounds measures of accuracy interaction and loop assessment that identify the pertinent open loop system factors affecting the particular performance aspect and thus provide unambiguous measures to aid system design additionally eigenvector scaling is introduced in order to tighten the bounds

reduced rank approximations to the far field transform in the gridded fast multipole method the fast multipole method fmm has been shown to have a reduced computational dependence on the size of finest level groups of elements when the elements are positioned on a regular grid and fft convolution is used to represent neighboring interactions however transformations between plane wave expansions used for fmm interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of fmm computations when finest level groups are large the transformation operators which are forward and inverse fourier transforms with the wave space confined to the unit sphere are smooth and well approximated using reduced rank decompositions that further reduce the computational dependence of the fmm on finest level group size the adaptive cross approximation aca is selected to represent the forward and adjoint far field transformation operators required by the fmm however the actual error of the aca is found to be greater than that predicted using traditional estimates and the aca generally performs worse than the approximation resulting from a truncated singular value decomposition svd to overcome these issues while avoiding the cost of a full scale svd the aca is employed with more stringent accuracy demands and recompressed using a reduced truncated svd the results show a greatly reduced approximation error that performs comparably to the full scale truncated svd without degrading the asymptotic computational efficiency associated with aca matrix assembly

on stochastic evolution equations for nonlinear bipolar fluids well posedness and some properties of the solution abstract we investigate the stochastic evolution equations describing the motion of a non newtonian fluids excited by multiplicative noise of levy type we show that the system we consider has a unique global strong solution we also give some results concerning the properties of the solution we mainly prove that the unique solution satisfies the markov feller property this enables us to prove by means of some results from ergodic theory that the semigroup associated to the unique solution admits at least an invariant measure which is ergodic and tight on a subspace of the lebesgue space l 2

guest editorial for the special issue on large and multiscale computational electromagnetics the 28 papers in this special issue focus on large and multiscale computational electromagnetics the issue starts with five papers on the finite difference time domain fdtd method then proceeds with five on the finite element method fem and eighteen on integral equation ie solvers the papers are briefly summarized here

pathwise global attractors for stationary random dynamical systems the asymptotic behaviour of random dynamical systems in polish spaces is considered under the assumption of existence of a random compact absorbing set assumption supposed to hold path by path a candidate pathwise attractora is defined the goal of the paper is to show that in the case of stationary dynamical systems a attracts bounded sets is measurable with respect to the algebra of invariant sets and is independent of when the system is ergodic an application to a general class of navier stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail

structured singular values with nondiagonal structures i characterizations the purpose of this two part series is to provide a robustness analysis framework for a class of problems with highly structured modeling uncertainties this framework is more general than that of the usual block diagonally structured uncertainties and it corresponds to a structure consisting of block by block matrix perturbations we study the structured singular value with respect to this structure and we establish a number of novel results for this notion this paper contains a study on the properties of the structured singular value we give an alternative characterization of this notion as the solution of a smooth optimization problem furthermore we show that under a certain circumstance the structured singular value reduces to a vector induced matrix norm

strong solution for a stochastic model of two dimensional second grade fluids existence uniqueness and asymptotic behavior abstract we investigate a stochastic evolution equation for the motion of a second grade fluid filling a bounded domain of r 2 global existence and uniqueness of strong probabilistic solution is established in contrast to previous results on this model we show that the sequence of galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem we also give two results on the long time behavior of the solution mainly we prove that the strong solution of our stochastic model converges exponentially in mean square to the stationary solution of the time independent second grade fluids equations if the deterministic part of the external force does not depend on time if the deterministic forcing term explicitly depends on time then the strong probabilistic solution decays exponentially in mean square

calculation of the structured singular value with a reduced number of optimization variables for the case of an n n uncertainty matrix with n sup 2 nonzero 1 1 blocks the structured singular value technique with similarity scaling suffers from the disadvantage of having to expand an n n matrix problem to an n sup 2 n sup 2 matrix optimization problem with n sup 2 1 free variables it is shown that for elementwise magnitude bounded uncertainties the structure of the problem may be exploited to yield a similarity scaling method which uses no more than 2 n 1 rather than n sup 2 1 independent optimization parameters a simple extension of this result shows that a reduction in the number of independent optimization variables is also possible for more general block structured uncertainties a more efficient implementation of the vector optimization method developed by m k h fan and a l tits 1986 is also proposed several examples are included to illustrate the results

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

the exponential behaviour and stabilizability of stochastic 2d navier stokes equations abstract some results on the pathwise exponential stability of the weak solutions to a stochastic 2d navier stokes equation are established the first ones are proved as a consequence of the exponential mean square stability of the solutions however some of them are improved by avoiding the previous mean square stability in some more particular and restrictive situations also some results and comments concerning the stabilizability and stabilization of these equations are stated

internal stabilization by noise of the navier stokes equation we show that the navier stokes equation in mathcal o subset r d d 2 3 around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller v t xi sum i 1 n v i t psi i xi dot beta i t xi in mathcal o where beta i i 1 n are independent brownian motions and psi i i 1 n is a system of functions on mathcal o with support in an arbitrary open subset mathcal o 0 subset mathcal o the stochastic control input v i i 1 n is found in feedback form the corresponding result for the linearized navier stokes equation was established in e barbu the internal stabilization by noise of the linearized navier stokes equation esaim control optim calc var to appear

the exponential stability for stochastic delay partial differential equations abstract in this paper we consider by the energy equality the exponential stability of energy solutions to a non linear stochastic functional partial differential equation with finite delay r 0 in separable hilbert spaces our method is very simple and is powerful for concrete stochastic delay partial differential equations

calculation of highly structured stability margins abstract the problem of assessing the robust stability of a closed loop system subject to plant uncertainty is addressed earlier techniques allow only a limited amount of structure information uncertainty and thus can often lead to conservative results a technique for increasing the bound over the stability margin is presented which may be applied together with the cross condition number to compute a stability margin for highly structured uncertainty regions a sample application is given to show the improvements that can be obtained by using the proposed technique in practical situations

m form numerical range and the computation of the structured singular value an equivalent expressions for the structures singular value is proposed leading to an alternative algorithm for its computation the approach is based to the geometric properties of the m form numerical range of certain tuples of matrices similar to previously considered schemes the algorithm proposed is proved to give the correct value for block structures of size up to three for larger sizes insight is gained into the question of the possible gap between the structured singular value and its known upper bound

software metamaterials transformation media based multiscale techniques for computational electromagnetics this paper presents computational models employing special transformation based media which we call software metamaterials for the purpose of enhancing the ability of numerical modeling methods for solving multi scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both the multi scale problems in general suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem the underlying idea in this study is to introduce transformation media into the computational domain of the finite element method or finite difference methods in order to allow uniform and easy to generate meshes by avoiding mesh refinement and therefore to develop efficient and simple computer aided simulation tools in other words a virtual equivalent problem is created which acts like the original problem the techniques proposed in this paper are validated via several finite element simulations in the context of tm z electromagnetic scattering problems

characterization of allowable perturbations for robust stability the problem of determining stability for a closed loop linear multivariable process in the presence of ill defined process perturbations is considered it is shown that m matrices may be used to characterize a class of allowable perturbations

on the equivalence between similarity and nonsimilarity scaling in robustness analysis in the analysis of multivariable systems in the presence of structured uncertainties similarity scaling and nonsimilarity scaling techniques have been independently proposed as methods for obtaining nonconservative robustness measures in order to fully exploit the unique advantages of each method it is desirable to obtain the required nonsimilarity scaling matrices directly from the associated similarity scaling matrix and vice versa without the need for separate optimizations the authors present an explicit relationship developed between the similarity and nonsimilarity scaling matrices from the optimal similarity scaling several applications of the results are also presented

characterization and efficient computation of the structured singular value the concept of structured singular value was recently introduced by doyle 1 as a tool for the analysis and synthesis of feedback systems with structured uncertainties it is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the h infty approach to control system design in this paper it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems properties of these optimization problems are exhibited leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3 and often does for block structures of larger size

robustness analysis of feedback systems with block diagonal structured uncertainties the results for magnitude bounded diagonal perturbation are extended to norm bounded block diagonal perturbation a useful consequence to this extension is that an easily computable upper bound for the structured singular value via suboptimal diagonal similarity scaling is obtained it is concluded that the results are applicable to a wider class of perturbations i e the norm which bounds the perturbation p in this study need not be the 2 norm maximum singular value in the scalar case this does not give much advantage as all pth norms reduce to the magnitude of the element however in the matrix case different norms would characterize different types of perturbations

minimizing the euclidean condition number this paper considers the problem of determining the row and or column scaling of a matrix a that minimizes the condition number of the scaled matrix this problem has been studied by many authors for the cases of the infty norm and the 1 norm the scaling problem was completely solved in the 1960s it is the euclidean norm case that has widespread application in robust control analyses for example it is used for integral controllability tests based on steady state information for the selection of sensors and actuators based on dynamic information and for studying the sensitivity of stability to uncertainty in control systems minimizing the scaled euclidean condition number has been an open question researchers proposed approaches to solving the problem numerically but none of the proposed numerical approaches guaranteed convergence to the true minimum this paper provides a convex optimization procedure to determine the scalings that minimize the euclidean condition number this optimization can be solved in polynomial time with off the shelf software

existence of global stochastic flow and attractors for navier stokes equations for 2 d stochastic navier stokes equations on the torus with multiplicative noise we construct a perfect cocycle and show the existence of global random compact attractors the equations considered do not admit a pathwise method of solution

the existence and asymptotic behaviour of energy solutions to stochastic 2d functional navier stokes equations driven by levy processes abstract let d be a bounded or unbounded open domain of 2 dimensional euclidean space r 2 if the boundary d exists then we assume that the boundary is smooth in this paper assuming that the kinematic viscosity 0 is large enough we discuss the existence and exponential stability of energy solutions to the following 2 dimensional stochastic functional navier stokes equation perturbed by the levy process d x t x t x t x t f t x t f t x t p d t d x t g t x t d w t u k t x t y q d t d y d i v x 0 in 0 d where x t x t x is the initial function for x d and t r 0 with r 0 it is assumed that f g f and k satisfy the lipschitz condition and the linear growth condition if there exists the boundary d then x t x 0 on 0 d

the exponential behavior of a stochastic globally modified cahn hilliard navier stokes model with multiplicative noise abstract in this article we study the stability of weak solutions to a stochastic version of a globally modified coupled cahn hilliard navier stokes model with multiplicative noise the model consists of the globally modified navier stokes equations for the velocity coupled with an cahn hilliard model for the order phase parameter we prove that under some conditions on the forcing terms the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions we also prove a result related to the stabilization of these equations

singular value and eigenvalue techniques in the analysis of systems with structured perturbations a new range of techniques is introduced for the purpose of exploiting information about the structure of the perturbation associated with uncertain linear multi variable feedback systems the class of perturbation considered is wide and ignores only the phase information of the individual elements of the perturbation matrix it encompasses diagonal block diagonal and other forms of block structured perturbations the techniques developed provide a means of assessing stability margins and also lead to an extension of the nyquist criterion

eigenvalue assignment robustness for systems with structured perturbations the eigenvalue assignment robustness problem of a linear time invariant uncertain system is considered allowable perturbations are obtained for ensuring the eigenvalues of a system with or without perturbations be retained in some distinct and arbitrarily shaped regions the presented criteria improve some of the previous results in the literature both for the transfer function model and the state space model

asymptotic behaviors of stochastic two dimensional navier stokes equations with finite memory the stochastic 2d navier stokes equations with finite memory are studied for the differentiable memory function the almost sure exponential stability of the weak solution is shown by employing a non negative semimartingale convergence argument for the nondifferentiable memory function the exponential stability in mean square for the weak solution is proved by using the differentiability property of the moment function

local uniformly upper semi continuity of random attractor for g navier stokes equation this paper is concerned with the locally uniform convergence from a family of pullback random attractors to a deterministic attractor we establish criteria by using joint pathwise convergence of the cocycles collective locally uniform compactness and eventually deterministic of the random attractors as an application of the abstract result it is shown that the family of random attractors for the stochastic g navier stokes equation is local uniformly upper semi continuous as the density of random noise tends to zero

convex and finite dimensional conditions for controller synthesis with dynamic integral constraints in this paper the problem of synthesizing controllers when the allowable disturbances and the cost criterion are defined via a finite number of matrix valued dynamic integral constraints is solved this allows one to design optimal control systems for plants subject to fixed input disturbances such as steps sinusoids and periodic disturbances disturbances of fixed and known spectrum disturbances defined as the set of signals in the kernel of a given operator and combinations thereof to penalize particular frequency components of the error variables in the control design process to penalize the maximum amplitude of an error variable and to consider other general cost criteria in the optimization and to solve a large class of robust control synthesis problems necessary and sufficient conditions for the general problem to have a solution are in terms of a computationally attractive finite dimensional linear matrix inequality

stochastic equations in hilbert space with application to navier stokes equations in any dimension abstract we give an existence theorem for an abstract nonlinear stochastic evolution equation in a hilbert space the result is applicable to the stochastic navier stokes equation in any dimension with a nonlinear noise term

necessary and sufficient stability criterion for systems with structured uncertainties the major principal direction alignment principle a necessary and sufficient stability criterion is proved for multivariable systems in the presence of element by element bounded perturbations the result constitutes a solution to the problem of computing the function for this class of perturbations and the paper also provides an explicit approximation to the exact criterion

robustness tests for feedback control systems using multidimensional uncertainty bounds a method is presented for proving the robustness of feedback controllers with respect to the stability requirement and design specifications on the i o behaviour of the closed loop systems the model uncertainties are described by multidimensional upper bounds hence the results are less conservative than those obtained by the singular value approach

the fast multipole method and fourier convolution for the solution of acoustic scattering on regular volumetric grids the fast multipole method fmm is applied to the solution of large scale three dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid the grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques the regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the fmm both of which scale linearly with the number of scattering elements in particular the use of fast fourier transforms to compute green s function convolutions required for neighboring interactions lowers the often significant cost of finest level fmm computations and helps mitigate the dependence of fmm cost on finest level box size numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest level box is increased

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

structured singular values with nondiagonal structures ii computation in part i we introduced a robust stability measure termed generalized structured singular value in part ii we address computational issues pertaining to this notion our main contribution is a computational method which would render the computation of the generalized structured singular value both more efficient and potentially more accurate as in the computation of the usual structured singular value the key in our method is to compute an upper norm bound scaled via a similarity transformation it is shown that this bound is as tight as those obtained elsewhere and that it can be computed considerably more efficiently furthermore it is shown that this bound is actually equal to the generalized structured singular value when the uncertainty has four blocks

navier stokes equations with delays some results on the existence and uniqueness of solutions to navier stokes equations when the external force contains some hereditary characteristics are proved