the h text p version of the finite element method for domains with curved boundaries this paper analyzes the convergence of the h text p version of the finite element method for elliptic problems on curved domains it proves that when the boundary of the domain is piecewise analytic boundary conditions are piecewise analytic and the sides of the elements are analytic the h text p version has an exponential rate of convergence numerical computations are included the paper generalizes the results previously obtained by the authors the h text p version of finite element method part 1 the basic approximation results comp mech 1 1986 pp 21 41 the h text p version of finite element method part 2 general results and applications comp mech 1 1986 pp 203 220

an analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems in this paper we study a novel parametrization for state space systems namely separable least squares data driven local coordinates slsddlc the parametrization by slsddlc has recently been successfully applied to maximum likelihood estimation of linear dynamic systems in a simulation study the use of slsddlc has led to numerical advantages in comparison to the use of more conventional parametrizations including data driven local coordinates ddlc however an analysis of properties of slsddlc which are relevant to identification has not been performed up to now in this paper we provide insights into the geometry and topology of the slsddlc construction and show a number of results which are important for actual identification in particular for maximum likelihood estimation we also prove that the separable least squares methodology is indeed guaranteed to be applicable to maximum likelihood estimation of linear dynamic systems in typical situations

optimal diagonal scaling for infinity norm optimization abstract a solution is presented for the previously unsolved diagonally scaled multivariable infinity norm optimization problem of minimizing d s a s s x s d 1 s over the set of stable minimum phase diagonal d s and stable x s this problem is of central importance in the synthesis of feedback control laws for robust stability and insensitivity in the presence of structured plant uncertainty the result facilitates the design of feedback controllers which optimize the excess stability margin 3 or equivalently the structured singular value 4 of diagonally perturbed feedback systems

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

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

an alternative solution to the h optimal control problems abstract in this paper we present an alternative solution to the problem min x h n n a bxc where a b rmand c are rational matrices in h n n the solution circumvents the need to extract the matrix inner factors of b and c providing a multivariable extension of sarason s h interpolation theory 1 to the case of matrix valued b s and c s the result has application to the diagonally scaled optimization problem int d a bxc d 1 where the infimum is over d x h n n d diagonal

well posedness of feedback systems insights into exact robustness analysis and approximate computations this paper establishes a framework for robust stability analysis of linear time invariant uncertain systems the uncertainty is assumed to belong to an arbitrary subset of complex matrices the concept used here is well posedness of feedback systems leading to necessary and sufficient conditions for robust stability based on this concept some insights into exact robust stability conditions are given in particular frequency domain and state space conditions for well posedness are provided in terms of hermitian form inequalities it is shown that these inequalities can be interpreted as small gain conditions with a generalized class of scalings given by linear fractional transformations lft using the lft scaled small gain condition in the state space setting the duality is established between the h sub spl infin norm condition with frequency dependent scalings and the parameter dependent lyapunov condition connections to the existing results including the structured singular value and the integral quadratic constraints are also discussed finally we show that our well posedness conditions can be used to give a less conservative yet computable bound on the real structured singular value this result is illustrated by numerical examples

performance of the h p version of the finite element method with various elements the paper addresses the performance of square elements of type q p and q p q p and q p are elements of degree p analogous to the well known 9 and 8 noded elements for p 2 the performance is analysed theoretically for the class of analytic functions numerical experiments confirm the conclusions drawn from the theory the computational complexity of a solution algorithm is studied using timings of the computation on an alliant fx 8 computer the data show that high order elements are very effective for the considered class of solutions

matchable observable linear models and direct filter tuning an approach to multivariable identification identification of linear time invariant multivariable systems can best be understood as comprising three separate problems selection of system model structure filter design and parameter estimation itself approaching the first using matchable observable models originally developed in the adaptive control literature and the second via direct or derivative free optimization effective least squares algorithms can be used for parameter estimation the accuracy robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data the results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature

robust stability analysis of time varying systems using time varying quadratic forms abstract we consider the robust stability of time varying linear systems subject to structured time varying uncertainty we provide an alternate proof of the result that robust stability holds if and only if a scaled small gain condition holds asymptotically the new proof employs an extension of the so called s procedure losslessness theorem to time varying quadratic forms which is of independent interest

efficient parallel implementations of finite element methods based on the conjugate gradient method in this paper we introduce a special way to store only the nonzero elements of the stiffness matrix to obtain an efficient parallel algorithm to solve partial differential equations with finite element method this storage method is obtained by considering the structure of the mesh and the form of the stiffness matrix the size of the matrix is the number of unknowns by a constant instead of the number of unknowns by the number of unknowns our method and algorithm are efficient in both time and memory experimental results are presented

variance analysis of identified linear miso models having spatially correlated inputs with application to parallel hammerstein models this contribution concerns variance analysis of linear multi input single output models when the inputs are temporally white but where different inputs may be correlated an expression is provided for the variance of a linearly parametrized estimate of the frequency response function from one block i e from one input to the output in particular this expression reveals that the variance increases in one block when the number of estimated parameters in another block is increased but levels off when the number of parameters in the other block reaches the number of parameters in the block in question it also quantifies exactly how correlation between inputs affects the resulting accuracy and a graphical representation is provided for this purpose the results are applicable to parallel miso hammerstein models when the nonlinearities are known and generalize an existing variance expression for this type of model

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

riemann hilbert approach to a generalised sine kernel and applications we investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval q q we determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its fredholm determinant further we apply our results to build the resolvent of truncated wiener hopf operators generated by holomorphic symbols finally the leading asymptotics of the fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models

quadratic stability with real and complex perturbations it is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear fractional unstructured perturbations does not hold when the perturbations are block structured for a limited class of problems quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms and hence appropriate synthesis techniques coupled with diagonal constant scalings can be used to design quadratically stable systems

robustness margin calculation with dynamic and real parametric uncertainty the problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics is considered a robust margin r sub m is defined and an algorithm to calculate r sub m and the closely related multivariable stability margin k sub m is developed how robust performance for real parametric uncertainty can be handled in this framework is also shown the result essentially provides a method to check whether or not the infinity norm of a closed loop transfer matrix is less than a specified level over a bounded set of real parametric variations

an lft approach to parameter estimation in this paper we consider a unified framework for parameter estimation problems under this framework the unknown parameters appear in a linear fractional transformation lft a key advantage of the lft problem formulation is that it allows us to efficiently compute gradients hessians and gauss newton directions for general parameter estimation problems without resorting to inefficient finite difference approximations the generality of this approach also allows us to consider issues such as identifiability persistence of excitation and convergence for a large class of model structures under a single unified framework

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

generalized mixed μ bounds for real and complex multiple block uncertainty with internal matrix structure new absolute stability results that unify and extend existing structured singular value bounds for mixed uncertainty are developed using frequency domain arguments these bounds generalize prior upper bounds for mixed by permitting the treatment of non diagonal real uncertain blocks as well as accounting for internal matrix structure in the uncertainty several specializations to well known absolute stability criteria from the classical literature are given which allow for a systematic comparison of these results in addressing the problem of robust stability for real parameter uncertainty

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

data driven local coordinates for multivariable linear systems and their application to system identification in this paper we introduce a new parametrization for state space systems data driven local coordinates ddlc the parametrization is obtained by restricting the full state space parametrization where all matrix entries are considered to be free to an affine plane containing a given nominal state space realization this affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state space systems at the nominal realization the application of the parametrization to prediction error identification is exemplified simulations indicate that the proposed parametrization has numerical advantages as compared to e g the more commonly used observable canonical form

duality in multiplier based robustness analysis frequency domain conditions involving multipliers are useful for robustness analysis the resulting analysis problem is generally convex but infinite dimensional and numerical solutions restricted to finite dimensional subspaces need to be considered the resulting finite dimensional problem can be transformed into a linear matrix inequality which can be solved using efficient algorithms the paper presents a format for the dual of the infinite dimensional problem the dual problem can be used to estimate the conservatism of particular finite dimensional subspaces

completely integrable equation for the quantum correlation function of nonlinear schrodinger equation correlation functions of exactly solvable models can be described by differential equations 1 in this paper we show that for the non free fermionic case differential equations should be replaced by integro differential equations we derive an integro differential equation which describes a time and temperature dependent correlation function of the penetrable bose gas the integro differential equation turns out to be the continuum generalization of the classical nonlinear schrodinger equation

model validation a connection between robust control and identification the gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data the model validation problem addressed is given experimental data and a model with both additive noise and norm bounded perturbations is it possible that the model could produce the observed input output data this problem is studied for the standard h sub infinity mu framework models a necessary condition for such a model to describe an experimental datum is obtained for a large class of models in the robust control framework this condition is computable as the solution of a quadratic optimization problem

geometry and integrability of topological antitopological fusion integrability of equations of topological antitopological fusion being proposed by cecotti and vafa describing the ground state metric on a given 2d topological field theory tft model is proved for massive tft models these equations are reduced to a universal form being independent on the given tft model by gauge transformations for massive perturbations of topological conformal field theory models the separatrix solutions of the equations bounded at infinity are found by the isomonodromy deformations method also it is shown that the ground state metric together with some part of the underlined tft structure can be parametrized by pluriharmonic maps of the coupling space to the symmetric space of real positive definite quadratic forms

brief paper constrained state space system identification with application to structural dynamics constrained identification of state space models representing structural dynamic systems is addressed based on physical insight transfer function constraints are formulated in terms of the state space parametrization a simple example shows that a method tailored for this application which utilizes the non uniqueness of a state space model outperforms the classic sequential quadratic programming method in terms of robustness and convergence properties the method is also successfully applied to real experimental data of a plane frame structure

on robust stability with structured time variant perturbations abstract we consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time invariant perturbations which are norm bounded the issue we address is the role that the type of perturbation norm plays in the robust stability conditions to this end the l p induced norm for 1 p on the perturbations is considered and it is shown that the structured singular value is the necessary and sufficient condition for robust stability for all these norms we conclude that for time invariant perturbations in contrast to the time varying case robust stability conditions are independent of the type of perturbation norms

a parametrization of all the unfalsified plant models for mimo systems the results of the parametrization of all the unfalsified models for single input single output systems are extended to multi input multi output mimo systems in this parametrization the assumed a priori plant and noise information are upper bounds of the h sub spl infin norm of the plant matrix valued transfer function and the noise magnitude the parametrization is on the basis of several series of plant time domain identification experiment data it is shown that for mimo systems all the unfalsified plant matrix valued transfer functions can still be expressed by the linear fractional transformation of a fixed matrix valued transfer function and an h sub spl infin norm bounded structure fixed but uncertain matrix valued transfer function however the high dimensions of the matrix valued transfer functions involved in the parametrization hamper the direct application of these results to robust controller design to overcome these difficulties further efforts are needed

a parallel finite element method for the analysis of crystalline solids abstract a parallel finite element method suitable for the analysis of 3d quasi static crystal plasticity problems has been developed the method is based on substructuring of the original mesh into a number of substructures which are treated as isolated finite element models related via the interface conditions the resulting interface equations are solved using a direct solution method the method shows a good speedup when increasing the number of processors from 1 to 8 and the effective solution of 3d crystal plasticity problems whose size is much too large for a single work station becomes possible

a numerical method for computing the structured singular value abstract this article suggests a new approach to computing doyle s structured singular value ssv of a matrix the ssv is a notion important in robust control and several iteration schemes exist for approximation a solution 1 2 4 8 10 11 our idea is to pick a special case of the general problem which we believe to be natural and give an algorithm for studying it based on off the shelf packages once we are committed to this special case we discuss a very general plant uncertainty problem it embraces real as well as complex plant perturbations of many kinds the idea is simple and we believe very natural to the problem

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

fast computation of the multivariable stability margin for real interrelated uncertain parameters an alternative implementation of an algorithm for the computation of the multivariable stability margin to check the robust stability of feedback systems with real parametric uncertainty is proposed this method eliminates the need for the frequency search by reducing it to the testing of a finite number of conditions these conditions have a special structure that allows a significant improvement in the speed of computation

brief paper new method for identifying finite degree volterra series in this paper the identification of a class of nonlinear systems which admits input output maps described by a finite degree volterra series is considered in actual fact it appears that this class can model many important nonlinear multivariable processes not only in engineering but also in biology socio economics and ecology to solve this identification problem we propose a method based on local gradient search in a local parameterization of the state space realization of finite degree volterra series with infinite horizon using the local parameterization not only reduces the amount of the gradient calculations to the minimal value but also overcomes the nonuniqueness problem of the optimal solution moreover we propose a sequential projection method to provide an initial estimation of the parameters of finite degree volterra series realization this initial estimation is used to initialize the gradient search method

similarity solutions of the deformed maxwell bloch system the authors have found similarity reductions for the deformed maxwell bloch system to the fifth and second painleve equations asymptotics of the solutions of these equations which are relevant to two level atomic systems with pumping have also been derived

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

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

a maximum modulus theorem for linear fractional transformations abstract a main result in the structured singular value theory is a maximum modulus like theorem for a special case of linear fractional transformations we extend that result to general linear fractional transformations

quantum and classical integrability new approaches in statistical mechanics abstract the present status of the statistical mechanics sm quantum and classical of integrable models is reviewed by reporting new results for their partition functions z obtained for anyon type models in one space and one time 1 1 dimensions the methods of functional integration developed already are extended further bose fermi equivalence and anyon descriptions are natural parts of the quantum theory and the anyon phase is quantised the classical integrability is exploited throughout and both classical and quantum integrability theory are reviewed this way and related to underlying algebraic structures notably the hopf algebras quantum groups a new q boson lattice gas is solved in this connection further results to be realised within 10 years concerning integrability integrable systems coupled to large dimensional chaos provided by a heat bath and their application in physics e g to high t c superconductivity are suggested

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

universal results for correlations of characteristic polynomials riemann hilbert approach we prove that general correlation functions of both ratios and products of characteristic polynomials of hermitian random matrices are governed by integrable kernels of three different types a those constructed from orthogonal polynomials b those constructed from cauchy transforms of the same orthogonal polynomials and finally c those constructed from both orthogonal polynomials and their cauchy transforms these kernels are related with the riemann hilbert problem for orthogonal polynomials for the correlation functions we obtain exact expressions in the form of determinants of these kernels derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via the deift zhou steepest descent stationary phase method for riemann hilbert problems and in particular to find negative moments of characteristic polynomials this reveals the universal parts of the correlation functions and moments of characteristic polynomials for an arbitrary invariant ensemble of 2 symmetry class

controller design for plants with structured uncertainty this paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structured plant uncertainty and bounded but unknown disturbances a general formulation for the performance robustness problem is presented and exact computable conditions are furnished these conditions are then utilized for synthesizing robust controllers which involves solving l1 optimization problems these solutions are computed using the duality theory of lagrange multipliers approximations and computational issues are discussed

dual field formulation of quantum integrable models equal time correlators are studied in completely integrable models the main example is the quantum non linear schrodinger equation introduction of an auxiliary fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

on computational complexity of invalidating structured uncertainty models abstract in this paper we study a class of uncertainty model validation invalidation problems for linear discrete time systems we consider models described by a linear fractional transformation lft of modeling uncertainties which are structured time invariant or time varying and are bounded in h or l 1 norms the experimental data available for use in invalidation are either input output time series observations or frequency response measurements we analyze the computational complexity associated with these problems while earlier work showed that for lft models with an unstructured uncertainty the invalidation problems can be reduced to one of solving linear matrix inequalities and hence may be tackled readily using well developed numerical methods in this paper we provide a simple proof to show that in the presence of structured uncertainties they are all np hard with respect to the number of uncertainty blocks suggesting that the problems are inherently intractable from a computational standpoint additionally we also demonstrate that the problems do become tractable when the lft model description is changed to an additive one leading to lmi based invalidation tests similar to those obtained elsewhere these results indicate that the main source of the computational difficulty lies in the lft description together with the structured nature of the uncertainties

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

complex analytic theory of the μ function in this paper we consider the determinant of the multivariable return difference nyquist map crucial in defining the complex m function as a holomorphic function defined on a polydisk of uncertainty the key property of holomorphic functions of several complex variables that is crucial in our argument is that it is an open mapping from this single result only we show that in the diagonal perturbation case all preimage points of the boundary of the horowitz template are included in the distinguished boundary of the polydisk in the block diagonal perturbation case where each block is norm bounded by one a preimage of the boundary is shown to be a unitary matrix in each block finally some algebraic geometry together with the weierstrass preparation theorem allows us to show that the deformation of the crossover under holomorphic variations of certain parameters is continuous q 1999 academic press

an implicit small gain condition and an upper bound for the real structured singular value in this paper we develop an upper bound for the real structured singular value that has the form of an implicit small gain theorem the implicit small gain condition involves a shifted plant whose dynamics depend upon the uncertainty set bound and unlike prior bounds does not require frequency dependent scales or multipliers numerical results show that the implicit small gain bound compares favorably with real bounds that involve frequency dependent scales and multipliers

systems with structured uncertainty relations between quadratic and robust stability the relation between the notions of robust stability and quadratic stability for uncertain systems with structured uncertainty due to both real and complex parameter variations is discussed examples are presented to demonstrate that for systems containing at least two uncertain blocks the notions of robust stability for complex parameter variations and quadratic stability for real parameter variations are not equivalent a byproduct of these examples is that for this class of systems quadratic stability for real perturbations need not imply quadratic stability for complex perturbations this is in stark contrast with the situation in the case of unstructured uncertainty for which it is known that quadratic stability for either real or complex perturbations is equivalent to robust stability for complex perturbations and thus equivalent to a small gain condition on the transfer matrix that the perturbation experiences

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

the direct linearization of a class of nonlinear evolution equations the paper deals with the direct linearization an approach used to generate particular solutions of the partial differential equations that can be solved through the inverse scattering transform linear integral equations are presented which enable one to find broad classes of solutions to certain nonlinear evolution equations in 1 1 and 2 1 dimensions

exact solvability and asymptotic aspects of generalized xx0 spin chains abstract building on our earlier work saeedian et al 2018 we introduce and study generalized xx0 models we explicitly construct a long range interacting spin chain referred to as the selberg model and study the correlation functions of the selberg and xx0 models using a matrix integral representation of the generalized xx0 model and applying asymptotic analysis in non intersecting brownian motion the phase structure of the selberg model is determined we find that tails of the tracy widom distribution of gaussian unitary ensemble govern a discrete to continuous third order phase transition in selberg model the same method also reproduces the gross witten phase transition of the original xx0 model finally we conjecture universal features for the phase structure of the generalized xx0 model

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

balanced canonical forms for system identification parameterizations of linear state space systems by balanced canonical forms are considered the structure in particular the topological properties of these parameterizations are investigated based on these results an algorithm for identification obtained by optimizing a likelihood type criterion function is proposed and analyzed in the algorithm both the estimation of real valued parameters and of integer parameters defining dynamic specification is incorporated the analysis of the algorithm emphasizes consistency results

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

some aspects of parallel implementation of the finite element method on message passing architectures abstract we discuss some aspects of implementing the finite element method on parallel computers with local memory and message passing in particular we compare the costs of using high order and low order elements and of direct and iterative solvers for solving the linear systems that occur our model of parallel computation is a two dimensional grid of processors chosen to be similar in shape to the underlying grid our main conclusions are that use of high order methods is an effective way to achieve high accuracy for some problems on both serial and parallel computers and that such methods provide a natural way to achieve efficiency in parallel implementations in addition we show that sparse direct solvers generalize naturally to methods based on high order elements and that direct solvers are adequate for two dimensional problems especially for multiple load vectors

temperature correlators of the impenetrable bose gas as an integrable system it is shown that the temperature equal time correlators of impenetrable bosons in one space dimension are described by a classical integrable system partial differential equations for two point as well as for multipoint correlators are obtained the short distance and low density expansions are constructed

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

extended matrix cube theorems with applications to µ theory in control in this paper we study semi infinite systems of linear matrix inequalities which are generically np hard for these systems we introduce computationally tractable approximations and derive quantitative guarantees of their quality as applications we discuss the problem of maximizing a hermitian quadratic form over the complex unit cube and the problem of bounding the complex structured singular value with the help of our complex matrix cube theorem we demonstrate that the standard scaling upper bound on m is a tight upper bound on the largest level of structured perturbations of the matrixm for which all perturbed matrices share a common lyapunov certificate for the discrete time stability

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

block ssor preconditionings for high order 3d fe systems ii incomplete bssor preconditionings abstract the solution of large linear systems resulting from hierarchical order p 2 p 5 finite element fe approximations of 3d equilibrium equations for orthotropic materials is considered the block ssor preconditioned cg method is applied to the reduced linear system with the schur complement obtained by eliminating internal degrees of freedom in accordance with a superelement partitioning as demonstrated by numerical results this strategy is much more efficient than the application of the corresponding bssor cg method to the original system and provides for efficient concurrent vector implementation to improve the solution method further the so called incomplete bssor preconditioning is suggested it is based on using incomplete cholesky factorizations of the matrix diagonal blocks instead of their true dense cholesky factors under a specific choice of incomplete factorizations related to the fe origination of the matrices in question the ibssor cg algorithm is shown to outperform the corresponding bssor cg algorithm with respect to both the total arithmetic costs and the efficiency of concurrent vector implementation

large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature abstract asymptotics of the temperature time dependent correlation function of two fields one dimensional bosons with infinite point like repulsion is calculated

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism

a study of the gap between the structured singular value and its convex upper bound for low rank matrices the size of the smallest structured destabilizing perturbation for a linear time invariant system can be calculated via the structured singular value spl mu the function spl mu can be bounded above by the solution of a convex optimization problem and in general there is a gap between spl mu and the convex bound this paper gives an alternative characterization of spl mu which is used to study this gap for low rank matrices the low rank characterization provides an easily computed bound which can potentially be significantly better than the standard convex bound this is used to find new examples with larger gaps than previously known

extensions of the small mu test for robust stability the notion of a topologically arcwise connected set is used to develop a general graph topology based robustness test the test provides a switching criterion among different inequality tests and possibly among different nominal models when it is applied to extend the small mu test the result reduces conservatism and allows a more natural application of the test

an analysis of the parametrization by data driven local coordinates for multivariable linear systems in this paper we study a novel parametrization for state space systems namely data driven local coordinates ddlc which have recently been introduced and applied even though ddlc has meanwhile become the default parametrization used in the system identification toolbox of the software package matlab an analysis of properties of ddlc which are relevant to identification has not been performed up to now in this paper we provide insights into the geometry and topology of the ddlc construction and show a number of results which are important for actual identification such as maximum likelihood type estimation