generalized factorization for daniele khrapkov matrix functions explicit formulas abstract explicit formulas for the canonical generalized factorization of a class of matrix functions of the daniele khrapkov class are derived the method followed in the paper is a modification of that used for the investigation of conditions for the existence of canonical factorization proposed in a previous paper by the same authors an example related to applications in diffraction theory is given

a parallel element by element solution scheme a parallel element by element scheme is developed for finite element solution of elliptic boundary value problems it is shown that for a broad class of computational grids the solution algorithm is totally parallelizable moreover the conversion of an existing serial ebe code to a parallel code is seen to be quite simple the method is implemented on the alliant fx 8 and sequent balance parallel computers and speedup performance studies are conducted for a representative elliptic pde in two dimensions the present procedure can be applied quite generally to other finite element applications and the associated programs can be modified in a straightforward way to implement the method

conjugate gradient solution of finite element equations on the ibm 3090 vector computer utilizing polynomial preconditionings abstract this paper presents the conjugate gradient solution of large finite element systems of equations on the ibm 3090 vf vector computer utilizing polynomial preconditionings these preconditionings are based on saad s least square polynomials applied to a scaled system of equations therefore for very ill conditioned systems the required amount of computation is reduced the matrix vector operations needed in the conjugate gradient iterations as well as in the construction of the preconditioners are computed at element level using an element by element solution scheme reordering the finite element mesh by a colouring algorithm and stacking the finite elements for vector processing the matrix operations are fully vectorized to best explore the high speed of the ibm 3090 vector facility the basic linear algebra subprograms available in the essl vector library were invoked in the test runs the numerical experiments provide the necessary support to efficiently use polynomial preconditionings in finite element applications

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

a robust control approach to perfect reconstruction of digital signals in this paper we present a deterministic worst case approach for reconstructing discrete valued signals that have been filtered via dispersive and noisy systems ldquochannelsrdquo this approach which is explored based on robust control ideas and makes no assumption on the noise distribution or structure other than a requirement that its magnitude be bounded can serve as a complement to existing approaches that attempt to reconstruct discrete valued signals by optimizing probabilistic criteria the particular problems touched upon are i necessary and sufficient conditions for causal possibly delayed perfect reconstruction under deterministic magnitude bounded noise for single input single output siso and multi input multi output mimo channels ii perfect reconstruction based on decision feedback df structures and iii necessary and sufficient conditions for perfect reconstruction with df structures in the presence of uncertainties in the channel the l1 control theory emerges as the natural key player for analysis and synthesis of perfect reconstructing strategies in this framework

subspace identification of circulant systems this article concerns the identification of a class of large scale systems called circulant systems circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation this property has been used in literature for control design and here we show how it can be used for system identification the approach that is proposed here will both reduce the complexity of the problem as well as provide models which have a circulant structure that can be exploited for control design a novel identification algorithm for circulant systems based on subspace identification is presented the algorithm is then tested in simulation on an academic example of circulant system and on a realistic finite element model of a vibrating plate

on a class of preconditioned iterative methods on parallel computers the standard implementations of iterative solvers for finite element and finite difference methods frequently use a diagonal jacobi preconditioner particularly for element by element schemes however for such methods the actual order of the condition number with respect to mesh size is not reduced by the preconditioner in the present paper we describe an iterative method where in addition the condition number is reduced by an order of magnitude moreover the scheme may also be implemented as an element by element method the method uses a generalized ssor preconditioner and a wave front or multi frontal ordering of the mesh nodes for a general irregular finite element mesh a striped irregular wave front ordering may be used the performance of the method as well as various iterative acceleration techniques for a parallel computer are examined in the numerical studies

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

segal wilson approach to integrable systems and riemann hilbert problems abstract in this paper a theory is developed for obtaining families of solutions to the kdv equation by formulating a riemann hilbert problem with an appropriate shift the theory builds on the classical work of segal and wilson 17 in which families of solutions are indexed on closed subspaces w of a space of functions on the unit circle admitting a direct sum decomposition h h h h h are subspaces of functions holomorphic respectively inside and outside the unit disk the theory developed in this paper lends itself easily to obtaining explicit solutions examples where the subspace w can be associated to soliton type solutions are considered more complex systems where singularities and riemann surfaces play a role are also presented in the last section the connection of our results to the function is analyzed the theory developed in this paper can easily be applied to other integrable systems and eventually to discrete integrable systems

on continuity properties of the two block l1 optimal design abstract this paper investigates continuity properties of the two block l 1 optimization resulting from the optimal design of bibo stability robustness for discrete time systems in the presence of coprime factor perturbations in general the two block l 1 optimal design might lack continuity properties since it might have no finite dimensional solution however this paper shows that for a suitable given truncated order the two block l 1 suboptimal design is continuous as a map from the plant to the suboptimal closed loop solution if the plant has no zeros on the unit circle and has a unique suboptimal solution furthermore if the set of plants is compactness we show that there exists a uniform bound on the degree of suboptimal solution for all plants in the set such that their deviation of suboptimal value from the optimal one have the same bound and the two block l 1 suboptimal design is uniformly continuous in particular in the case in which the plant has nonunique solution a procedure is also developed on how to choose a solution that preserves continuity the results enable the stability of robust l 1 adaptive scheme to hold in the presence of coprime factor perturbations

a comparison between lqr control for a long string of siso systems and lqr control of the infinite spatially invariant version in this paper we consider a long string of siso systems which in the limit becomes a scalar infinite spatially invariant system we compare the lqr control for long but finite strings with the lqr control for the corresponding infinite strings we give analytical and numerical examples where these are quite different and we investigate the cause in addition we obtain sufficient conditions for the lqr solutions to be similar as the length of the string increases

on slowly time varying systems abstract a characterization of stabilizing controllers for slowly time varying systems based on input output descriptions of the plant and the controller is presented this approach generalizes standard results on slowly time varying systems with finite dimensional state space representation and allows both the plant and the controller to be infinite dimensional the controller design will be based on frozen time versions of the plant obtained at equally spaced instances in time

on the control and estimation over relative sensing networks in this note we consider certain structural aspects of estimation and control over relative sensing networks rsns in this venue using tools from basic algebraic graph theory namely the incidence matrix and cut and cycle spaces of a connect graph we examine transformations among relative sensing topologies for a networked system these transformations are parameterized for noise free as well as noisy networks and their utility in the context of network centric robust control and control reconfigurations is explored

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

explicit wiener hopf factorization and nonlinear riemann hilbert problems a method for explicit wiener hopf factorization of 2 2 matrix valued functions is presented together with an abstract definition of a class of functions c q 1 q 2 to which it applies the method involves the reduction of the original factorization problem to certain nonlinear scalar riemann hilbert problems which are easier to solve the class c q 1 q 2 contains a wide range of classes dealt with in the literature including the well known daniele khrapkov class the structure of the factors in the factorization of any element of the class c q 1 q 2 is studied and a relation between the two columns of the factors which gives one of the columns in terms of the other through a linear transformation is established this greatly simplifies the complete determination of the factors and gives relevant information on the nature of the factorization two examples suggested by applications are completely worked out

a distributed memory parallel element by element scheme for semiconductor device simulation abstract a domain decomposition and parallel element by element ebe scheme is developed for semiconductor device simulation modeled by the drift diffusion dd equations a classical gummel iterative decoupling of the potential and carrier transport equations is applied on an unstructured triangulation the distributed memory ebe scheme is formulated for a galerkin finite element approximation of the nonlinear poisson problem and a modified scharfetter gummel method is used for the carrier transport problem the resulting sequences of symmetric and nonsymmetric linear systems are solved via preconditioned krylov methods unstructured triangular grids are used to permit grading of the mesh which is then partitioned to processor subdomains with appropriate data structures for message passing details of the parallel algorithm and data structure are provided the scheme is implemented in fortran90 with mpi and performance results are presented for a representative mosfet on an ibm sp a cray t3e and an sgi cray origin2000

factorization in a torus and riemann hilbert problems abstract a new concept of meromorphic factorization for holder continuous functions defined on a contour that is the pullback of r or the unit circle in a riemann surface of genus 1 is introduced and studied and its relations with holomorphic factorization are discussed it is applied to study and solve some scalar riemann hilbert problems in and vectorial riemann hilbert problems in c including wiener hopf matrix factorization as well as to study some properties of a class of toeplitz operators with 2 2 matrix symbols

integration of hp adaptivity and a two grid solver for elliptic problems we present implementation details and analyze convergence of a two grid solver forming the core of the fully automatic hp adaptive strategy for elliptic problems the solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp refinement the classical v cycle algorithm combines an overlapping block jacobi smoother with optimal relaxation and a direct solve on the coarse grid a simple theoretical analysis is illustrated with extensive numerical experimentation

3 d large scale wave propagation modeling by spectral element method on cray t3e multiprocessor highly efficient algorithms and massively parallel computers are needed for acoustic full wave modeling in large scale 3 d realistic unbounded media in this work a spectral element method in conjunction with a new iterative solution technique is presented the very high spatial accuracy of the algorithm allows for increased computational efficiency when compared to standard finite element method in addition the use of an iterative solver based on a local element by element formulation and a matrix vector product which is factored and converted to a faster matrix matrix product allows for a significant reduction both in storage requirements and in the computational complexity the resulting algorithm can easily be implemented on high performance vector and or parallel processors the numerical scheme has been tested on a cray t3e supercomputer our experimental results show that efficiency is very high and that good load balancing can be obtained at run time because relevant blocks of computations are performed at the element level and are totally independent

local global double algebras for slow h sup infinity adaptation ii optimization of stable plants for pt i see ibid vol 36 no 2 p 130 42 1991 the authors presently establish an explicit formula linking global and local sensitivity for systems with stable plants in which local sensitivity is a lipschitz continuous function of data frequency domain estimates of time domain sensitivity norms which become accurate as rates of time variation approach zero are obtained notions of adaptive versus nonadaptive robust control are introduced it is shown that adaptive control can achieve better sensitivity than optimal nonadaptive control it is demonstrated that in general h sup infinity optimal interpolants do not depend lipschitz continuously on data however delta suboptimal interpolants of the aak central maximal entropy type are shown to satisfy a tractable lipschitz condition

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

a deterministic solver for a hybrid quantum classical transport model in nanomosfets we model a nanomosfet by a mesoscopic time dependent coupled quantum classical system based on a sub band decomposition and a simple scattering operator we first compute the sub band decomposition and electrostatic force field described by a schrodinger poisson coupled system solved by a newton raphson iteration using the eigenvalue eigenfunction decomposition the transport in the classical direction for each sub band modeled by semiclassical boltzmann type equations is solved by conservative semi lagrangian characteristic based methods numerical results are shown for both the thermodynamical equilibrium and time dependent simulations in typical nowadays nanomosfets

distributed control of systems over discrete groups this paper discusses distributed controller design and analysis for distributed systems with arbitrary discrete symmetry groups we show how recent results for designing controllers for spatially interconnected systems based on semidefinite programming are applicable to a much larger class of interconnection topologies we also show how to exploit the structure of the symmetry group to produce a hierarchy of decreasingly conservative analysis and synthesis conditions

block and full matrix ilu preconditioners for parallel finite element solvers parallel finite element solvers based on ilu preconditionings are developed implemented and tested in two and three dimensional laplace problems the computational domain is decomposed into n subdomains for parallel processing the structure of the parallel computer system consists of the main processor and n satellite processors two algorithms are developed a block ilu preconditioner at the subdomain level without communication between the satellite processors and a full matrix ilu preconditioner coupling the subdomain degrees of freedom and requiring communication between the satellite processors different node orderings mesh sizes and number of satellite processors are tested the efficiency of both block and full matrix ilu preconditioners is strongly dependent on the node ordering inside each subdomain the finite elements in each subdomain must be connected

parallel algorithms for elliptic equations we describe a number of parallel algorithms for the numerical solution of elliptic equations and present some implementations on the denelcor hep parallel processor the equations we study typical of those encountered in a range of fluid pressure equations are of the form where the coefficient tensor may represent a density permeability or dielectric constant we allow the possibility of discontinuities in and of line and point sources in f the equations are discretized using finite elements with orders ranging from linear to bicubic we use a tree of increasingly fine grids to achieve parallelism in the course of mesh refinement we use conjugate gradient methods as well as multigrid methods to solve the resulting algebraic equations within each subgrid we describe the implementation of these methods as parallel algorithms and present results of actual performance on the hep computer in each case we demonstrate near optimal performance on the hep as measured by speedup over the corresponding serial algorithm we would like to thank both argonne national laboratory and ballistic research laboratory for allowing us access to their hep computers the operations staffs at both sites gave us unstintingly of their time even when called on after hours this research on an at times quite temperamental machine would never have been completed without their help we would also like to thank argonne national laboratory for the excellent two day hep introduction provided us prior to the start of this research finally we wish to thank e lusk and r overbeek for providing us with copies of their hep macros

optimal rejection of persistent and bounded disturbances continuity properties and adaptation continuity properties of the problem of optimal rejection of bounded persistent disturbances otherwise known as l sup 1 optimal control are furnished for discrete time single input single output systems it is shown that for any plant with no zeros on the unit circle the l sup 1 optimal design is continuous as a map from the plant to the optimal closed loop solution if the plant has a unique optimal solution in the case of nonuniqueness a superoptimal criterion is proposed that will always lead to a unique solution however it still fails to supply continuity a characterization of a general class of adaptive controllers in the presence of bounded disturbances is given using this characterization an adaptive robust scheme based on the l sup 1 design methodology is proposed and it is shown to be globally convergent

structural optimization based on preconditioned conjugate gradient analysis methods an efficient method for structural optimization is presented instead of classical direct decomposition methods preconditioned conjugate gradient pcg methods in conjunction with two proposed starting vector generation schemes are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems these inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization this technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints the effectiveness of the pcg methods of analysis in structural optimization is demonstrated comparison among different preconditioners is made the effect of the proposed starting vector generation schemes is shown the comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis when using pcg methods of analysis are assessed the parallel computation potential of pcg methods is discussed because of the iterative nature of pcg analysis methods and the prospects they offer for parallel computation it is found that pcg analysis methods show promise in the context of structural optimization

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

extension of parrott s theorem to nondefinite scalings in this paper the matrix version of parrott s theorem is extended to encompass nondefinite scalings this extension can be used to relax the causality requirements for many linear matrix inequality based synthesis problems

supervisory control of uncertain linear time varying systems we consider the problem of adaptively stabilizing linear plants with unknown time varying parameters in the presence of noise disturbances and unmodeled dynamics using the supervisory control framework which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time time varying uncertain linear plants can be stabilized by supervisory control provided that the plant s parameter varies slowly enough in terms of mixed dwell time switching and average dwell time switching the noise and disturbances are bounded and small enough in terms of l infinity norms and the unmodeled dynamics are small enough in the input to state stability sense this work extends previously reported works on supervisory control of linear time invariant systems with constant unknown parameters to the case of linear time varying uncertain systems a numerical example is included and limitations of the approach are discussed

a parallel deterministic solver for the schrodinger poisson boltzmann system in ultra short dg mosfets comparison with monte carlo abstract we present a parallel deterministic solver for the boltzmann schrodinger poisson system for partially confined dg mosfets our 2d model uses a dimensional coupling the electrons behave as particles along the longitudinal dimension and as waves along the transverse dimension in ben abdallah et al 2009 the authors validated in a simplified setting the solver for the eigenproblems in this paper we have focused on obtaining physically accurate results by introducing a realistic si conduction band and electron phonon interactions we have switched from cartesian to elliptic variables for the wave vector and consequently radically rebuilt the time integrator the code has been parallelized following a domain decomposition approach the results have been compared to those given by a monte carlo solver

comparison between element edge and compressed storage schemes for iterative solutions in finite element analyses this paper is concerned with optimization techniques for the iterative solution of sparse linear systems arising from finite element discretization of partial differential equations three different data structures are used to store the coefficient matrices the usual element based data structure the compressed storage row format and the edge based approach a comparison between these storage schemes is performed quantifying for most common linear elements the number of floating points operations indirect addressing and memory requirements necessary to perform matrix vector products the overall performance of the preconditioned conjugate gradient method is measured for different situations involving 2d and 3d diffusion and elasticity problems highlighting the pros and cons of each storage scheme

robust adaptive control a slowly varying systems approach in this paper we characterize a class of indirect adaptive controllers that can stabilize a time invariant system subjected to both parametric and l to l bounded unstructured uncertainty pertaining to this class of controllers a particular indirect adaptive scheme is proposed and an a priori computable upper bound on the size of the unstructured uncertainty for which stability is ensured is provided

adaptive control of spatially invariant systems a slowly varying approach we present a general class of adaptive controllers for spatially invariant systems based on certainty equivalence approach at each step the plant is estimated via the distributed projection algorithm as presented in sarwar that guarantees to result in a gradually varying spatiotemporal estimated plant for large enough time given an instance in space and time the estimated plant is thought of as a linear spatially invariant system with the defining operators fixed at that time and space instance the spatiotemporal local controllers assumed to exist are designed to stabilize the corresponding frozen linear spatially invariant systems we show that as long as the rates of spatiotemporal variations of the estimated plant and the spatiotemporal controller eventually become sufficiently small a globally stable adaptive scheme can be guaranteed

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

identification of spatiotemporally invariant systems for control adaptation we present a distributed projection algorithm for system identification of spatiotemporally invariant systems with the ultimate purpose of utilizing it in an indirect adaptive control scheme each subsystem communicates only with its immediate neighbors to share its current estimate along with a cumulative improvement index on the basis of the cumulative improvement index the best estimate available is picked in order to carry out the next iteration for small estimation error the scheme switches over to a smart averaging routine the proposed algorithm guarantees to bring the local estimates arbitrarily close to one another developing a local consensus which makes it amenable to control by the application of indirect distributed adaptive control schemes it is also shown through simulations that the proposed algorithm has a clear advantage over the standard projection algorithm our proposed algorithm is also suitable for addressing the estimation problem in distributed networks that arise in a variety of applications such as environment monitoring target localization and potential sensor network problems

factorization of a class of symbols with outer functions abstract in this paper the wiener hopf or riemann hilbert factorization of a class of symbols important in applications is studied the symbols in this class involve outer functions that appear in applications such as diffraction by strip gratings and infinite dimensional integrable systems the method proposed is based on the reduction of a vector riemann hilbert to a scalar problem on an appropriate riemann surface two examples are given leading to the riemann sphere and to an elliptic curve

an analysis of element by element preconditioners for nonsymmetric problems abstract a group of preconditioners for systems of linear equations arising from finite element discretization which is of increasing interest is the class of element by element preconditioners these preconditioners allow the solution of a system without the need to assemble the global stiffness matrix the success of a preconditioner depends on how much it reduces the condition number of the global stiffness matrix in this paper a bound on the condition number of the preconditioned stiffness matrix is derived in terms of norms of the element stiffness matrices the element preconditioning matrices and the flexibility matrix ideas are proposed how to improve the element by element preconditioner

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

polynomial preconditioners for conjugate gradient calculations dubois greenbaum and rodrigue proposed using a truncated neumann series as an approximation to the inverse of a matrix a for the purpose of preconditioning conjugate gradient iterative approximations to ax b if we assume that a has been symmetrically scaled to have unit diagonal and is thus of the form i g then the neumann series is a power series in g with unit coefficients the incomplete inverse was thought of as a replacement of the incomplete cholesky decomposition suggested by meijerink and van der vorst in the family of methods iccg n the motivation for the replacement was the desire to have a preconditioned conjugate gradient method which only involved vector operations and which utilized long vectors we here suggest parameterizing the incomplete inverse to form a preconditioning matrix whose inverse is a polynomial in g we then show how to select the parameters to minimize the condition number of the product of the polynomial and i g theoretically the resulting algorithm

matrix riemann hilbert problems and factorization on riemann surfaces abstract the wiener hopf factorization of 2 2 matrix functions and its close relation to scalar riemann hilbert problems on riemann surfaces is investigated a family of function classes denoted c q 1 q 2 is defined to each class c q 1 q 2 a riemann surface is associated so that the factorization of the elements of c q 1 q 2 is reduced to solving a scalar riemann hilbert problem on for the solution of this problem a notion of factorization is introduced and a factorization theorem is presented an example of the factorization of a function belonging to the group of exponentials of rational functions is studied this example may be seen as typical of applications of the results of this paper to finite dimensional integrable systems

an element by element solution algorithm for problems of structural and solid mechanics abstract it is proposed to solve large scale finite element equation systems arising in structural and solid mechanics by way of an element by element approximate factorization technique which obviates the need for a global coefficient matrix the procedure has considerable operation count and i o advantages over direct elimination schemes and it is easily implemented numerical results demonstrate the effectiveness of the method and suggest its potential for the analysis of large scale systems

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

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

a factorisation procedure for two by two matrix functions on the circle with two rationally independent entries the aim of this paper is the explicit canonical or standard factorisation of matrix functions with wiener algebra elements the present approach covers all regular 2 2 matrices where two entries are arbitrary and the remaining two are linear combinations of the former with rational coefficient functions it is based on the knowledge of how to factorise scalar functions and rational matrix functions in general one also needs the approximation of any scalar wiener algebra function with a rational function however this can be easily circumvented in many applications by intuitive manipulations with rational matrix functions

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

efficient deterministic parallel simulation of 2d semiconductor devices based on weno boltzmann schemes a flexible parallel deterministic solver of the boltzmann poisson system for 2d semiconductor device simulation on computer clusters is presented the simulator is obtained by parallelizing a previously proposed numerical scheme based on high order finite difference weighted essentially non oscillatory weno schemes although the underlying numerical scheme presents important advantages over direct simulation monte carlo methods this scheme imposes very high demands of computing power due to this the parallelization of the different calculation phases in the numerical scheme has been tackled the data subdomain which demands most