crossed products of nuclear c algebras and their traces abstract this work addresses the blackadar kirchberg question bkq as it pertains to group and reduced crossed product c algebras the bkq asks if every stably finite c algebra admits the matricial field mf property we characterize the mf property for a class of reduced crossed product c algebras and for their traces we prove that every ordered abelian group is in a sense mf and show that there is no k theoretic obstruction to an affirmative answer to the bkq using classification techniques and induced k theoretic dynamics we give an affirmative answer to the bkq for reduced crossed products of ah algebras of real rank zero by free groups combining our results with recent progress in elliott s classification program shows that the reduced crossed product of a separable simple unital nuclear uct and monotracial c algebra by the free group is always mf we also examine traces on these crossed products and show they always admit certain finite dimensional approximation properties by appealing to a result of ozawa rordam and sato we show that semidirect products of discrete amenable groups by free groups admit mf reduced group c algebras

an adaptive tracking problem with a control input constraint abstract in this paper we consider the problem of controlling an uncertain linear time invariant lti continuous time plant when there is a control input constraint a switching controller is presented which will carry out asymptotic error regulation for constant reference and constant disturbance signals which are compatible with the control input constraint assuming that i the plant is asymptotically stable ii the plant has no transmission zeros at zero and iii the plant has as many inputs as outputs this controller is quite easy to implement especially in the single input single output siso case and is noise tolerant some examples including a model of a three input three output distillation column are included to illustrate the controller behaviour

a novel multigrid based preconditioner for heterogeneous helmholtz problems an iterative solution method in the form of a preconditioner for a krylov subspace method is presented for the helmholtz equation the preconditioner is based on a helmholtz type differential operator with a complex term a multigrid iteration is used for approximately inverting the preconditioner the choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with fourier analysis multigrid analysis results are verified by numerical experiments high wavenumber helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner

brief low gain integral control of continuous time linear systems subject to input and output nonlinearities continuous time low gain integral control strategies are presented for tracking of constant reference signals for finite dimensional continuous time asymptotically stable single input single output linear systems subject to a globally lipschitz and non decreasing input nonlinearity and a locally lipschitz non decreasing and affinely sector bounded output nonlinearity both non adaptive but possibly time varying and adaptive integrator gains are considered in particular it is shown that applying error feedback using an integral controller ensures asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is ultimately sufficiently small and c the reference value is feasible in a very natural sense the classes of actuator and sensor nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone

integral control of infinite dimensional linear systems subject to input saturation closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is shown to ensure asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is sufficiently small and c the reference value is feasible in a very natural sense the class of actuator nonlinearities under consideration contains standard nonlinearities important in control engineering such as saturation and deadzone

non fragile observer based sliding mode control for markovian jump systems with mixed mode dependent time delays and input nonlinearity this paper is concerned with the state estimation and the sliding mode control smc for a class of markovian jump systems with mixed mode dependent time delays and input nonlinearity a non fragile observer is designed to estimate the system states and an observer based smc is synthesized to ensure the reachability of the sliding surfaces in the state estimation space by constructing a novel mode dependent lyapunov krasovskii functional some new criteria are established for the existence and the solvability of the desired observer based sliding mode controller finally numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results

further properties of lp dimension abstract this article establishes more properties of the l p dimension introduced in a previous article given an amenable group acting by translation on l p a number satisfying dimension like properties is associated to the usually infinite dimensional subspaces y of l p which are invariant under the action of this may be interpreted as a von neumann dimension for l p spaces as a consequence for p 1 2 if y is a closed non trivial invariant subspace of l p and let y n be an increasing sequence of closed invariant subspace such that y n l p v then there exist a k such that y k y 0

a triangulation algorithm for fast elliptic solvers based on domain imbedding the following triangulation problem is considered let r be a rectangle and omega an open domain whose closure is contained in r consider a rectangular grid covering r perturb this grid by shifting points close to the boundary partial omega onto partial omega this results in a quadrilateral almost rectangular grid divide each cell of this grid into two triangles along one of its diagonals this results in a triangulation of r a subset of this triangulation is a triangulation of an approximation omega h to omega the distance between partial omega h and partial omega is required to be o h 2 where h denotes the maximum meshwidth of the rectangular grid all triangles should be nondegenerate triangulations of this kind are needed for finite element domain imbedding methods for elliptic boundary value problems a particularly simple example of such a method is reviewed the convergence theory for this method motivates our definition of nondegeneracy of triangles f

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity abstract the problem of non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control a novel control law is established such that the sliding surface in the state estimation space can be reached in a finite time and chattering reduction is obtained a sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality lmi finally a simulation example is presented to show the validity and advantages of the proposed method

on groups with quasidiagonal c algebras abstract we examine the question of quasidiagonality for c algebras of discrete amenable groups from a variety of angles we give a quantitative version of rosenberg s theorem via paradoxical decompositions and a characterization of quasidiagonality for group c algebras in terms of embeddability of the groups we consider several notable examples of groups such as topological full groups associated with cantor minimal systems and abels celebrated example of a finitely presented solvable group that is not residually finite and show that they have quasidiagonal c algebras finally we study strong quasidiagonality for group c algebras exhibiting classes of amenable groups with and without strongly quasidiagonal c algebras

on sofic actions and equivalence relations abstract the notion of sofic equivalence relation was introduced by gabor elek and gabor lippner their technics employ some graph theory here we define this notion in a more operator algebraic context starting from connes embedding problem and prove the equivalence of these two definitions we introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic we also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic

fictitious domain methods for the numerical solution of two dimensional scattering problems fictitious domain methods for the numerical solution of two dimensional scattering problems are considered the original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary first order second order and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries the finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes and the discrete equations are solved with fictitious domain methods a special finite element method using nonmatching meshes is considered this method uses the macro hybrid formulation based on domain decomposition to couple polar and cartesian coordinate systems a special preconditioner based on fictitious domains is introduced for the arising algebraic saddle point system such that the subspace of constraints becomes invariant with respect to the preconditioned iterative procedure the performance of the new method is compared to the fictitious domain methods both with respect to accuracy and computational cost

a new application of random matrices ext c _ mathrm red f_2 is not a group in the process of developing the theory of free probability and free entropy voiculescu introduced in 1991 a random matrix model for a free semicircular system since then random matrices have played a key role in von neumann algebra theory cf v8 v9 the main result of this paper is the following extension of voiculescui s random matrix result let x n 1 x n r be a system of r stochastically independent n i n gaussian self adjoint random matrices as in voiculescui s random matrix paper v4 and let x1 xr be a semi circular system in a c probability space then for every polynomial p in r noncommuting variables lim niaeia p x n 1 o x n r o p x1 xr for almost all o in the underlying probability space we use the result to show that the ext invariant for the reduced c algebra of the free group on 2 generators is not a group but only a semi group this problem has been open since anderson in 1978 found the first example of a c algebra a for which ext a is not a group

guaranteed cost synchronization of chaotic cellular neural networks with time varying delay synchronization of cellular neural networks with time varying delay is discussed in this letter based on razumikhin theorem a guaranteed cost synchronous controller is given unlike lyapunov krasovskii analysis process there is no constraint on the change rate of time delay the saturated terms emerging in the razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by lipschitz condition and vector inequality which will bring more conservatism then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form with the help of a sufficient and necessary transformation condition the minimization of the guaranteed cost is studied and a further criterion for getting the controller is presented finally the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time varying delay cellular neural networks

stability analysis and fail safe operation of inverters operated in parallel in this paper the stability in the sense of boundedness of inverters operated in parallel is proven and the fail safe operation is achieved for generic linear or nonlinear loads described in the generalised dissipative hamiltonian form the robust droop controller rdc recently proposed in the literature for achieving accurate proportional power sharing and tight voltage regulation is implemented in a nonlinear matrix form to achieve a bounded inverter voltage and inherit a fail safe capability using nonlinear lyapunov methods it is proven that the rdc with fail safe approximates the original rdc generates a bounded inverter output voltage within the given technical limits and guarantees nonlinear closed loop system stability in the sense of boundedness when the prescribed limits are violated e g due to sensor failure the proposed method rapidly shuts down in a continuous time manner thus disconnecting the inverter to prevent a complete system failure even when the protection circuit fails extensive simulation results are presented to demonstrate this approach for two single phase paralleled inverters feeding a linear and a nonlinear load under a sensor failure scenario

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

second order absorbing boundary conditions for the wave equation a solution for the corner problem the treatment of domains with corners in the problem of absorbing boundary conditions for the wave equation is very important from a practical point of view a technical difficulty appears as soon as conditions of order greater than or equal to 2 are considered a solution is proposed for the two dimensional case when second order conditions are used this solution consists of prescribing an adequate corner condition the problem thus obtained is analyzed theoretically and the condition is proved to be optimal the results obtained here are illustrated by numerical simulations some extensions to higher space dimensions and higher order conditions are proposed

entropy and the variational principle for actions of sofic groups recently lewis bowen introduced a notion of entropy for measure preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy by applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants and we establish the variational principle in this context in the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group c algebra

a damping preconditioner for time harmonic wave equations in fluid and elastic material a physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering the earlier preconditioners for the helmholtz equation are generalized for elastic materials and three dimensional domains an algebraic multigrid method is used in approximating the inverse of damped operators several numerical experiments demonstrate the behavior of the method in complicated two dimensional and three dimensional domains

integral control of linear systems with actuator nonlinearities lower bounds for the maximal regulating gain closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is known to ensure asymptotic tracking of constant reference signals provided that 1 the steady state gain of the linear part of the plant is positive 2 the positive integrator gain is sufficiently small and 3 the reference value is feasible in a very natural sense here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step response and second order systems with a time delay in the input or output the lower bounds are given in terms of open loop frequency step response data and the lipschitz constant of the nonlinearity and are hence readily obtainable

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

dynamical approximation entropies and topological entropy in operator algebras dynamical entropy invariants based on a general approximation approach are introduced for c and w algebra automorphisms this includes a noncommutative extension of topological entropy

sofic equivalence relations we introduce the notion of sofic measurable equivalence relations using them we prove that connes embedding conjecture as well as the measurable determinant conjecture of luck sauer and wegner hold for treeable equivalence relations

a domain decomposition solver for acoustic scattering by elastic objects in layered media a finite element solution procedure is presented for accurately computing time harmonic acoustic scattering by elastic targets buried in sediment an improved finite element discretization based on trilinear basis functions leading to fourth order phase accuracy is described for sufficiently accurate discretizations 100 million to 1 billion unknowns are required the resulting systems of linear equations are solved iteratively using the gmres method with a domain decomposition preconditioner employing a fast direct solver due to the construction of the discretization and preconditioner iterations can be reduced onto a sparse subspace associated with the interfaces numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths

a parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension a parallel fast direct solution method for linear systems with separable block tridiagonal matrices is considered such systems appear for example when discretizing the poisson equation in a rectangular domain using the five point finite difference scheme or the piecewise linear finite elements on a triangulated possibly nonuniform rectangular mesh the method under consideration has the arithmetical complexity mathcal o n log n and it is closely related to the cyclic reduction method but instead of using the matrix polynomial factorization the so called partial solution technique is employed hence in this paper the method is called the partial solution variant of the cyclic reduction method pscr method the method is presented and analyzed in a general radix q framework and based on this analysis the radix 4 variant is chosen for parallel implementation using the mpi standard the generalization of the method to the case of arbitrary block dimension is described the numerical experiments show the sequential efficiency and numerical stability of the pscr method compared to the well known blktri implementation of the generalized cyclic reduction method the good scalability properties of the parallel pscr method are demonstrated in a distributed memory cray t3e 750 computer

modified integration rules for reducing dispersion error in finite element methods abstract this paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time harmonic wave propagation problems the method involves a simple shift of the integration points to locations away from conventional gauss or gauss lobatto integration points for bilinear rectangular elements such a shift results in fourth order accuracy with respect to dispersion error error in wavelength as opposed to the second order accuracy resulting from conventional integration numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements

time varying and adaptive integral control of infinite dimensional regular linear systems with input nonlinearities closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz nondecreasing actuator nonlinearity and compensated by an integral controller with time dependent gain k t is shown to ensure asymptotic tracking of a constant reference signal r provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the function t mapsto k t monotonically decreases to zero at a sufficiently slow rate this result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under conditions a and b

absolute stability and integral control absolute stability results of both circle criterion and popov type are derived for finite dimensional linear plants with non linearity in the feedback loop the linear plant contains an integrator and so is not asymptotically stable the possibly time varying non linearity satisfies a particular sector condition which allows for cases with zero lower gain such as saturation and deadzone the conjunction of stable but not asymptotically stable linear plants and non linearities with possibly zero lower gain is a distinguishing feature of the paper the absolute stability results are invoked in proving convergence and stability properties of low gain integral feedback control for tracking of constant reference signals in the context of exponentially stable linear systems subject to input and output non linearities

a composite preconditioner for the electromagnetic scattering from a large cavity in this paper we propose a composite preconditioner for the electromagnetic scattering from a large cavity the electromagnetic cavity problem is described by the helmholtz equation with a nonlocal boundary condition on the aperture of the cavity and dirichlet or neumann boundary conditions on the walls of the cavity the preconditioner proposed here combines the optimal sine transform based approximation with a layered medium model using fast fourier transforms the computational cost of every iteration is o n 2logn on an nxn uniform partition of the unit square numerical results for a model problem show that the new preconditioner is more efficient than those recently considered in the literature for the cavity with a small portion of non layered media we propose a sparse preconditioned conjugate orthogonal conjugate gradient solver combined with the new preconditioner numerical results for a model problem are reported to demonstrate the efficiency of the sparse solver

a domain decomposition method for the helmholtz equation in a multilayer domain the two dimensional helmholtz equation for problems where the physical domain consists of layers with different material properties is studied an efficient preconditioner for iterative solution of the problem is constructed the problem is discretized with fourth order accurate finite difference operators for the construction of the radiation boundary conditions a fourth order finite element method also is used the large sparse complex indefinite and ill conditioned system of equations that arises is solved with preconditioned restarted gmres a domain decomposition method is used in which the preconditioning is based on the schur complement algorithm with fast poisson type preconditioners for the subdomains the memory requirements for the preconditioner are nearly linear in the number of unknowns the arithmetic complexity for each iteration is low whereas the construction of the preconditioner is a bit more expensive electromagnetic wave propagation in a three layered waveguide is used as a model problem numerical experiments show that convergence is achieved in a few iterations compared with banded gaussian elimination which is a standard solution method the iterative method shows significant gain in both memory requirements and arithmetic complexity furthermore the relative gain grows when the problem size increases

the norm of polynomials in large random and deterministic matrices let bf x n x 1 n ldots x p n be a family of n n independent normalized random matrices from the gaussian unitary ensemble we state sufficient conditions on matrices bf y n y 1 n ldots y q n possibly random but independent of xn for which the operator norm of p bf x n bf y n bf y n converges almost surely for all polynomials p limits are described by operator norms of objects from free probability theory taking advantage of the choice of the matrices yn and of the polynomials p we get for a large class of matrices the no eigenvalues outside a neighborhood of the limiting spectrum phenomena we give examples of diagonal matrices yn for which the convergence holds convergence of the operator norm is shown to hold for block matrices even with rectangular gaussian blocks a situation including non white wishart matrices and some matrices encountered in mimo systems

an algebraic multigrid based shifted laplacian preconditioner for the helmholtz equation a preconditioner defined by an algebraic multigrid cycle for a damped helmholtz operator is proposed for the helmholtz equation this approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties the spectral properties of the preconditioned systems and the convergence of the gmres method are studied with linear quadratic and cubic finite element discretizations numerical experiments are performed with two dimensional problems describing acoustic scattering in a cross section of a car cabin and in a layered medium asymptotically the number of iterations grows linearly with respect to the frequency while for lower frequencies the growth is milder the proposed preconditioner is particularly effective for low frequency and mid frequency problems

an lp version of von neumann dimension for banach space representations of sofic groups abstract in 5 a gournay defined a notion of l p dimension for invariant subspaces of l q n with amenable the number dim l q l p v is dim v when p q and is preserved by a certain class of equivariant bounded linear isomorphisms we develop a notion of dim l p y where y is a banach space with a uniformly bounded action of a sofic group and is a sofic approximation in particular our definition makes sense for a large class of non amenable groups we also develop a notion of dim s p y with an r embeddable group and s p the space of finite dimensional schatten p class operators these numbers are invariant under bounded equivariant linear isomorphisms and under the natural translation action of dim l p l p v dim v and dim s p l p v dim v for 1 p 2 in particular this shows that l p v is not isomorphic to l p w as a representation of if dim v dim w and is r embeddable we discuss other concrete computations in a follow up paper including proving that our dimension agrees with von neumann dimension for representations contained in a multiple of the left regular representation

a riesz basis methodology for proportional and integral output regulation of a one dimensional diffusive wave equation in this article we consider a dam river system modeled by a diffusive wave equation this model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important in order to stabilize and regulate the system we propose a proportional and integral boundary controller contrary to many physical systems we end up with a nondissipative closed loop system with noncollocated actuators and sensors we show that the closed loop system is a riesz spectral system and generates an analytic semigroup then we shall be able to assign the spectrum of the closed loop system in the open left half plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation these results are illustrated by several numerical examples

a multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations standard multigrid algorithms have proven ineffective for the solution of discretizations of helmholtz equations in this work we modify the standard algorithm by adding gmres iterations at coarse levels and as an outer iteration we demonstrate the algorithm s effectiveness through theoretical analysis of a model problem and experimental results in particular we show that the combined use of gmres as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200 for fixed wave numbers it displays grid independent convergence rates and has costs proportional to the number of unknowns

high performance modeling acoustic and elastic waves using the parallel dichotomy algorithm a high performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media an initial boundary value problem is replaced by a series of boundary value problems for a constant elliptic operator and different right hand sides via the integral laguerre transform it is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the gmres k method for modeling elastic waves a preconditioning operator was the laplace operator that is inverted using the variable separation method the novelty of the proposed algorithm is using the dichotomy algorithm 26 which was designed for solving a series of tridiagonal systems of linear equations in the context of the preconditioning operator inversion via considering analytical solutions it is shown that modeling wave processes for long instants of time requires high resolution meshes the proposed parallel fine mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy by solving model problems it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors from 2 to 8192

numerical solution of the nonlinear helmholtz equation using nonorthogonal expansions in j comput phys 171 2001 632 677 we developed a fourth order numerical method for solving the nonlinear helmholtz equation which governs the propagation of time harmonic laser beams in media with a kerr type nonlinearity a key element of the algorithm was a new nonlocal two way artificial boundary condition abc set in the direction of beam propagation this two way abc provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain altogether the algorithm of j comput phys 171 2001 632 677 has allowed for a direct simulation of nonlinear self focusing without neglecting nonparaxial effects and backscattering to the best of our knowledge this capacity has never been achieved previously in nonlinear optics in the current paper we propose an improved version of the algorithm the principal innovation is that instead of using the dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation we now introduce sommerfeld type local radiation boundary conditions which are constructed directly in the discrete framework numerically implementation of the sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non hermitian matrix subsequently the separation of variables which is a key building block of the aforementioned nonlocal abc is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance as well as in the range of physical phenomena that it is capable of simulating

brief paper ultimate bounded stability and stabilization of linear systems interconnected with generalized saturated functions this paper proposes some ultimate bounded stability analysis and stabilization conditions for systems involving actuators with different nonlinear elements like for instance both saturation and dead zone or both saturation and stick slip results are based on the use of a convex differential inclusion approach indeed an adequate property allowing to upper bound some product terms related to the nonlinearity is provided thus constructive conditions associated to convex optimization schemes are developed to determine suitable regions of the state space in which the closed loop trajectories can be captured

bounded integral control of input to state practically stable nonlinear systems to guarantee closed loop stability a fundamental problem in control systems theory is that stability is not always guaranteed for a closed loop system even if the plant is open loop stable with the only knowledge of the input to state practical stability isps of the plant in this note a bounded integral controller bic is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed loop system stability in the sense of boundedness when a given bound is required for the control output an analytic selection of the bic parameters is proposed and its performance is investigated using lyapunov methods extending the result for locally isps plant systems additionally it is shown that the bic can replace the traditional integral controller ic and guarantee asymptotic stability of the desired equilibrium point under certain conditions with a guaranteed bound for the solution of the closed loop system simulation results of a dc dc buck boost power converter system are provided to compare the bic with the ic operation

numerical solution of electromagnetic scattering from a large partly covered cavity the paper focuses on the numerical study of electromagnetic scattering from two dimensional 2d large partly covered cavities which is described by the helmholtz equation with a nonlocal boundary condition on the aperture the classical five point finite difference method is applied for the discretization of the helmholtz equation and a linear approximation is used for the nonlocal boundary condition we prove the existence and uniqueness of the numerical solution when the medium in the cavity is y direction layered or the number of the mesh points on the aperture is large enough the fast algorithm proposed in bao and sun 2005 2 for open cavity models is extended to solving the partly covered cavity problem with vertically layered media a preconditioned krylov subspace method is proposed to solve the partly covered cavity problem with a general medium in which a layered medium model is used as a preconditioner of the general model numerical results for several types of partly covered cavities with different wave numbers are reported and compared with those by ilu type preconditioning algorithms our numerical experiments show that the proposed preconditioning algorithm is more efficient for partly covered cavity problems particularly with large wave numbers