weak strong uniqueness of dissipative measure valued solutions for polyconvex elastodynamics for the equations of elastodynamics with polyconvex stored energy and some related simpler systems we define a notion of a dissipative measure valued solution and show that such a solution agrees with a classical solution with the same initial data when such a classical solution exists as an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution also for a system of conservation laws endowed with a positive and convex entropy we show that dissipative measure valued solutions attain their initial data in a strong sense after time averaging

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

quasiconvex elastodynamics weak strong uniqueness for measure valued solutions a weak strong uniqueness result is proved for measure valued solutions to the system of conservation laws arising in elastodynamics the main novelty brought forward by the present work is that the underlying stored energy function of the material is assumed strongly quasiconvex the proof employs tools from the calculus of variations to establish general convexity type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

behavioral controllability of delay differential systems in this paper we will prove that the system described by the delay differential equation r d dt delta w 0 with delta the unit delay operator is controllable if and only if the rank of r lambda e lambda is constant for all lambda in bkc this condition is compared with the existing results obtained both by the analytic approach and by the algebraic approach to delay differential systems

model order reduction with oblique projections for large scale wave propagation there are many applications in which it is necessary to solve large scale parametrized wave propagation problems repeatedly this is still quite a challenging task even with the largest available computer clusters in this paper we will discuss the application of model order reduction mor to problems in seismic petroleum exploration with the aim of diminishing the necessary computing time by a significant factor we consider pod and some variants pod is a model order reduction technique that uses snapshots of a few simulations in order to quickly compute related problems with similar accuracy the method of lines via a petrov galerkin approximation that uses the snapshots as basis functions is the considered approach the order reduction comes from projecting the wave equation discretized in space to the subspace spanned by the snapshots this has been shown earlier to work well in two dimensions the challenge in three dimensions comes from the size of the spatial meshes required and the fact that the method usually requires a number of snapshots that do not fit in fast memory even for current high end multicore machines parallelization is not an option since it is already used for other aspects of this massive problem

a variational approximation scheme for three dimensional elastodynamics with polyconvex energy we construct a variational approximation scheme for the equations of three dimensional elastodynamics with polyconvex stored energy the scheme is motivated by some recently discovered geometric identities qin 18 for the null lagrangians the determinant and cofactor matrix and by an associated embedding of the equations of elastodynamics into an enlarged system which is endowed with a convex entropy the scheme decreases the energy and its solvability is reduced to the solution of a constrained convex minimization problem we prove that the approximating process admits regular weak solutions which in the limit produce a measure valued solution for polyconvex elastodynamics that satisfies the classical weak form of the geometric identities this latter property is related to the weak continuity properties of minors of jacobian matrices here exploited in a time dependent setting

exact observability and controllability for linear neutral type systems the problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach the duality with the exact controllabil ity problem is the main tool it is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system a nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator the characterization of the duality between controllability and observability is deduced and then observability conditions are obtained

lsmr an iterative algorithm for sparse least squares problems an iterative method lsmr is presented for solving linear systems ax b and least squares problems min ax b 2 with a being sparse or a fast linear operator lsmr is based on the golub kahan bidiagonalization process it is analytically equivalent to the minres method applied to the normal equation a t ax a t b so that the quantities a t r k are monotonically decreasing where r k b ax k is the residual for the current iterate x k we observe in practice that r k also decreases monotonically so that compared to lsqr for which only r k is monotonic it is safer to terminate lsmr early we also report some experiments with reorthogonalization

lsrn a parallel iterative solver for strongly over or underdetermined systems we describe a parallel iterative least squares solver named textttlsrn that is based on random normal projection textttlsrn computes the min length solution to min x in mathbb r n a x b 2 where a in mathbb r m times n with m gg n or m ll n and where a may be rank deficient tikhonov regularization may also be included since a is involved only in matrix matrix and matrix vector multiplications it can be a dense or sparse matrix or a linear operator and lsrn automatically speeds up when a is sparse or a fast linear operator the preconditioning phase consists of a random normal projection which is embarrassingly parallel and a singular value decomposition of size lceil gamma min m n rceil times min m n where gamma is moderately larger than 1 e g gamma 2 we prove that the preconditioned system is well conditioned with a strong concentration result on the extreme singular values and hence that the number of iterations is fully predictable

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

weak strong uniqueness for measure valued solutions to the ericksen leslie model equipped with the oseen frank free energy abstract we analyze the ericksen leslie system equipped with the oseen frank energy in three space dimensions recently the author introduced the concept of measure valued solutions to this system and showed the global existence of these generalized solutions in this paper we show that suitable measure valued solutions which fulfill an associated energy inequality enjoy the weak strong uniqueness property i e the measure valued solution agrees with a strong solution if the latter exists the weak strong uniqueness is shown by a relative energy inequality for the associated nonconvex energy functional

strong traces for solutions of multidimensional scalar conservation laws in this paper we consider multidimensional scalar conservation laws without bv estimates defined in a subset d we show that with a non degeneracy hypothesis on the flux we can define a strong notion of trace at the boundary of reached by l 1 convergence

finding structure with randomness probabilistic algorithms for constructing approximate matrix decompositions low rank matrix approximations such as the truncated singular value decomposition and the rank revealing qr decomposition play a central role in data analysis and scientific computing this work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low rank matrix approximation these techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets this paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions these methods use random sampling to identify a subspace that captures most of the action of a matrix the input matrix is then compressed either explicitly or implicitly to this subspace and the reduced matrix is manipulated deterministically to obtain the desired low rank factorization in many cases this approach beats its classical competitors in terms of accuracy robustness and or speed these claims are supported by extensive numerical experiments and a detailed error analysis the specific benefits of randomized techniques depend on the computational environment consider the model problem of finding the k dominant components of the singular value decomposition of an m times n matrix i for a dense input matrix randomized algorithms require bigo mn log k floating point operations flops in contrast to bigo mnk for classical algorithms ii for a sparse input matrix the flop count matches classical krylov subspace methods but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures iii for a matrix that is too large to fit in fast memory the randomized techniques require only a constant number of passes over the data as opposed to bigo k passes for classical algorithms in fact it is sometimes possible to perform matrix approximation with a single pass over the data

delay independent stabilization of linear systems stabilization of delayed linear systems by state variable feedback is studied in this paper the assignability of the decaying rate of these systems is also considered the conditions obtained are applicable to systems with time varying delays without any restriction the basis of these conditions is a criterion for delay independent stability of linear system previously obtained it is shown that in some cases a system is delay independent stabilizable although a decaying rate is not assignable for this system

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

onsager s conjecture in bounded domains for the conservation of entropy and other companion laws we show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy and other respective companion laws if they possess a certain fractional differentiability of order one third in the interior of the domain and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary this extends various recent results of the authors

randomized core reduction for discrete ill posed problem abstract in this paper we apply randomized algorithms to approximate the total least squares tls solution of the problem a x b in the large scale discrete ill posed problems a regularization technique based on the multiplicative randomization and the subspace iteration is proposed to obtain the approximate core problem in the error analysis we provide upper bounds for the errors of the solution and the residual of the randomized core reduction illustrative numerical examples and comparisons are presented

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

localised relative energy and finite speed of propagation for compressible flows abstract for the incompressible and the isentropic compressible euler equations in arbitrary space dimension we establish the principle of localised relative energy thus generalising the well known relative energy method to this end we adapt classical arguments of c dafermos to the euler equations we give several applications to the behaviour of weak solutions like local weak strong uniqueness local preservation of smoothness and finite speed of propagation for the isentropic system

reachability of a class of infinite dimensional linear systems an external approach with applications to general neutral systems this paper studies the question of quasi approximate reachability of the standard observable realizations of pseudorational impulse responses introduced by the author the framework places the current theory of retarded and neutral delay differential systems into a unified input output framework several necessary and sufficient conditions for quasi reachability are derived in particular new criteria for quasireachability and eigenfunction completeness are obtained for general delay differential systems with no restriction on the type of delays furthermore as a byproduct the theory leads to necessary and sufficient conditions for approximate left coprimeness of matrices with distribution entries examples are discussed to illustrate the theory

quadratic stabilizability of linear systems with structural independent time varying uncertainties the author investigates the problem of designing a linear state feedback control to stabilize a class of single input uncertain linear dynamical systems the systems under consideration contain time varying uncertain parameters whose values are unknown but bounded in given compact sets the method used to establish asymptotical stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the author first shows that to ensure a stabilizable system some entries of the system matrices must be sign invariant he then derives necessary and sufficient conditions under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the conditions show that all uncertainties can only enter the system matrices in such a way as to form a particular geometrical pattern called an antisymmetric stepwise configuration for the systems satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example

large scale inverse model analyses employing fast randomized data reduction when the number of observations is large it is computationally challenging to apply classical inverse modeling techniques we have developed a new computationally efficient technique for solving inverse problems with a large number of observations e g on the order of 107 or greater our method which we call the randomized geostatistical approach rga is built upon the principal component geostatistical approach pcga we employ a data reduction technique combined with the pcga to improve the computational efficiency and reduce the memory usage specifically we employ a randomized numerical linear algebra technique based on a so called sketching matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis in this way the computational and memory costs for rga scale with the information content rather than the size of the calibration data our algorithm is coded in julia and implemented in the mads open source high performance computational framework http mads lanl gov we apply our new inverse modeling method to invert for a synthetic transmissivity field compared to a standard geostatistical approach ga our method is more efficient when the number of observations is large most importantly our method is capable of solving larger inverse problems than the standard ga and pcga approaches therefore our new model inversion method is a powerful tool for solving large scale inverse problems the method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity

global asymptotic stability of nonlinear delayed systems of neutral type abstract global asymptotic stability of delayed differential equation of neutral type with off diagonally increasing right hand side is considered first it is shown that by using a special form of variable transformation the considered system can be reduced to a differential difference inequality of retarded type the stability of the trivial solution of the given system is studied with the help of thus obtained inequality this is a development of the approach previously presented by ma et al however the condition so far obtained on the nonlinear cases by ma et al nonlinear anal theory methods appl 33 4 1998 367 is rather restrictive and these restrictions are somewhat similar to those for linear systems in short the nonlinear cone of invariant region with the origin as its head constructed by nonlinear functions must contain a linear cone inside it the object of this report is to remove such restriction

on the function space controllability of linear neutral systems a criterion is derived for approximate controllability of linear autonomous neutral functional differential equations in the sobolev space w 2 1 h 0 mathbb e n controllability conditions are based on an abstract evolution equation representation of the system an abstract criterion applicable to a general class of neutral systems is obtained and for the special case of matrix systems of the form frac d dt left x t a 1 x t h right e 0 x t e 1 x t h bu t this abstract criterion leads to an algebraic criterion

further condition for the delay independent stabilization of linear systems there are two different conditions for the delay independent stabilization of linear systems by means of state variable feedback including no delays one of which is also sufficient for decay rate assignability in this paper a wider condition is presented for delay independent stabilization it is proved that this condition includes the conditions so far obtained

low rank approximation and regression in input sparsity time we design a new distribution over m n matrices s so that for any fixed n d matrix a of rank r with probability at least 9 10 psaxp2 e 1 e paxp2 simultaneously for all x rd here m is bounded by a polynomial in re 1 and the parameter e 0 1 such a matrix s is called a subspace embedding furthermore sa can be computed in o nnz a time where nnz a is the number of nonzero entries of a this improves over all previous subspace embeddings for which computing sa required at least ndlog d time we call these s sparse embedding matrices using our sparse embedding matrices we obtain the fastest known algorithms for overconstrained least squares regression low rank approximation approximating all leverage scores and ep regression more specifically let b be an n 1 vector e 0 a small enough value and integers k p g 1 our results include the following regression the regression problem is to find d 1 vector x for which pax bpp l 1 e min xpax bpp for the euclidean case p e 2 we obtain an algorithm running in o nnz a o d3e 2 time and another in o nnz a log 1 e o d3 log 1 e time here o f e f log o 1 f for p 1 more generally we obtain an algorithm running in o nnz a log n o r e 1 c time for a fixed c low rank approximation we give an algorithm to obtain a rank k matrix k such that pa kpf 1 e p a akpf where ak is the best rank k approximation to a that is ak is the output of principal components analysis produced by a truncated singular value decomposition useful for latent semantic indexing and many other statistical problems our algorithm runs in o nnz a o nk2e 4 k3e 5 time leverage scores we give an algorithm to estimate the leverage scores of a up to a constant factor in o nnz a log n o r3 time

a fast randomized algorithm for orthogonal projection we describe an algorithm that given any full rank matrix a having fewer rows than columns can rapidly compute the orthogonal projection of any vector onto the null space of a as well as the orthogonal projection onto the row space of a provided that both a and its adjoint a can be applied rapidly to arbitrary vectors as an intermediate step the algorithm solves the overdetermined linear least squares regression involving a and may therefore be used for this purpose as well in many circumstances the technique can accelerate interior point methods for convex optimization including linear programming see for example chapter 11 of s j wright primal dual interior point methods siam philadelphia 1997 the basis of the algorithm is an obvious but numerically unstable scheme typically known as the method of normal equations suitable use of a preconditioner yields numerical stability we generate the preconditioner rapidly via a randomized procedure that succeeds with extremely high probability we provide numerical examples demonstrating the superior accuracy of the randomized method over direct use of the normal equations

initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws we consider initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws through the scalar case the entropy solutions we address assume their initial data only in the sense of weak star in l as t 0 and satisfy the entropy inequality in the sense of distributions for t 0 we prove that if the flux function has weakly genuine nonlinearity then the entropy solutions are always unique and the initial layers do not appear we also discuss applications to the zero relaxation limit for hyperbolic systems of conservation laws with relaxation

weak strong uniqueness for measure valued solutions we prove the weak strong uniqueness for measure valued solutions of the incompressible euler equations these were introduced by diperna and majda in their landmark paper commun math phys 108 4 667 689 1987 where in particular global existence to any l2 initial data was proven whether measure valued solutions agree with classical solutions if the latter exist has apparently remained open

bezout identities and common minor zeros of 2 d polynomial matrices and applications to time delay systems this paper is concerned with factor zero coprimeness of 2 d polynomial matrices and studies relating bezout identities and some of their properties first we show that a pair of factor coprime matrices satisfies the particular bezout identities which are useful for feedback stabilization secondly we investigate the properties of the common minor zeros common zeros of all the maximum minors of factor coprime factorizations of 2 d transfer function matrices finally we apply the results to time delay systems of neutral or retarded type and provide tests for the spectrally controllability canonicality

paper linear ultimate boundedness control of uncertain dynamical systems given a state equation whose description includes uncertain parameters it is often desirable to design a feedback controller which renders all solutions uniformly and ultimately bounded when facing such a problem one often has available or assumes an upper bound for the excursions of the uncertain parameters within this framework the objective is to guarantee no matter how nature selects the uncertainty that the state will eventually end up and remain within some pre specified region when this region is a small neighborhood about the origin the concept of uniform ultimate boundedness is tantamount to practical asymptotic stability the objectives of this paper are twofold first and foremost our goal is to show that a class of ultimate boundedness problems which have been solved to date via nonlinear control can in point of fact be solved via linear control this is the main result and is given in theorem 4 1 secondly we show that some of the so called matching assumptions which have been required in the earlier literature can be weakened somewhat this enables one to design controllers for a larger class of dynamical systems than previously considered

the analysis of exact controllability of neutral type systems by the moment problem approach the problem of exact null controllability is considered for a wide class of linear neutral type systems with distributed delay the main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families a complete characterization of this problem is given the minimal time of controllability is specified the results are based on the analysis of the riesz basis property of eigenspaces of the neutral type systems in hilbert space

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order the spectral theory for linear autonomous neutral functional differential equations fde yields explicit formulas for the large time behaviour of solutions our results are based on resolvent computations and dunford calculus applied to establish explicit formulas for the large time behaviour of solutions of fde we investigate in detail a class of two dimensional systems of fde

statistical solutions of hyperbolic conservation laws foundations we seek to define statistical solutions of hyperbolic systems of conservation laws as time parametrized probability measures on p integrable functions to do so we prove the equivalence between probability measures on l p spaces and infinite families of correlation measures each member of this family termed a correlation marginal is a young measure on a finite dimensional tensor product domain and provides information about multi point correlations of the underlying integrable functions we also prove that any probability measure on a l p space is uniquely determined by certain moments correlation functions of the equivalent correlation measure we utilize this equivalence to define statistical solutions of multi dimensional conservation laws in terms of an infinite set of equations each evolving a moment of the correlation marginal these evolution equations can be interpreted as augmenting entropy measure valued solutions with additional information about the evolution of all possible multi point correlation functions our concept of statistical solutions can accommodate uncertain initial data as well as possibly non atomic solutions even for atomic initial data for multi dimensional scalar conservation laws we impose additional entropy conditions and prove that the resulting entropy statistical solutions exist are unique and are stable with respect to the 1 wasserstein metric on probability measures on l 1

controllability radii of linear neutral systems under structured perturbations abstractin this paper we shall deal with the problem of calculation of the controllability radii of linear neutral systems of the form x t a0x t a1x t h a 1x t h bu t we will derive the definition of exact controllability radius approximate controllability radius and euclidean controllability radius for this system by using multi valued linear operators the computable formulas for these controllability radii are established in the case where the system s coefficient matrices are subjected to structured perturbations some examples are provided to illustrate the obtained results

a statistical perspective on randomized sketching for ordinary least squares we consider statistical as well as algorithmic aspects of solving large scale least squares ls problems using randomized sketching algorithms for a ls problem with input data x y rn p rn sketching algorithms use a sketching matrix s rr n where r n then rather than solving the ls problem using the full data x y sketching algorithms solve the ls problem using only the sketched data sx sy prior work has typically adopted an algorithmic perspective in that it has made no statistical assumptions on the input x and y and instead it has been assumed that the data x y are fixed and worst case wc prior results show that when using sketching matrices such as random projections and leverage score sampling algorithms with p r n the wc error is the same as solving the original problem up to a small constant from a statistical perspective we typically consider the mean squared error performance of randomized sketching algorithms when data x y are generated according to a statistical linear model y x e where e is a noise process in this paper we provide a rigorous comparison of both perspectives leading to insights on how they differ to do this we first develop a framework for assessing in a unified manner algorithmic and statistical aspects of randomized sketching methods we then consider the statistical prediction efficiency pe and the statistical residual efficiency re of the sketched ls estimator and we use our framework to provide upper bounds for several types of random projection and random sampling sketching algorithms among other results we show that the re can be upper bounded when p r n while the pe typically requires the sample size r to be substantially larger lower bounds developed in subsequent results show that our upper bounds on pe can not be improved

from conservative to dissipative systems through quadratic change of time with application to the curve shortening flow we provide several examples of dissipative systems that can be obtained from conservative ones through a simple quadratic change of time a typical example is the curve shortening flow in mathbb r d which is a particular case of mean curvature flow with a co dimension higher than one except in the case d 2 through such a change of time this flow can be formally derived from the conservative model of vibrating strings obtained from the nambu goto action using the concept of relative entropy or modulated energy borrowed from the theory of hyperbolic systems of conservation laws we introduce a notion of generalized solutions that we call dissipative solutions for the curve shortening flow for given initial conditions the set of generalized solutions is convex and compact if not empty smooth solutions to the curve shortening flow are always unique in this setting

uniform ultimate boundedness of the solutions of uncertain dynamic delay systems with state dependent and memoryless feedback control a continuous feedback controller is developed for a class of non linear time varying uncertain systems governed by functional differential equations with retarded arguments the form of the controller guarantees that under certain assumptions all solutions are uniformly bounded in norm for time t sufficiently largo in spite of the uncertainty in system parameters and input signals furthermore given any 0 the parameters in the description of the controller can be chosen such that the closed loop solutions all satisfy x t for large t

delay independent stabilization and decay rate assignability of linear systems with limited measurable state variables delay independent stabilization and decay rate assignability of linear systems with limited measurable state variables are considered to construct control signals 2n dimensional linear systems including no delays are introduced the conditions obtained for delay independent stabilization are contained in systems with measurable state presented previously the conditions obtained for decay rate assignability for systems with measurable state variables are also sufficient for the present system

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

on the delay independent stabilization of linear neutral systems with limited measurable state variables abstract the delay independent stabilizability of linear neutral systems with limited measurable state variables is considered a sufficient condition for the delay independent stabilizability of linear retarded systems with limited measurable state variables and linear neutral systems with measurable state variables which had been obtained by amemiya and maet al is proved to be also valid for linear neutral systems with limited measurable state variables

relative entropy for hyperbolic parabolic systems and application to the constitutive theory of thermoviscoelasticity we extend the relative entropy identity to the class of hyperbolic parabolic systems whose hyperbolic part is symmetrizable the resulting identity in the general theory is useful for providing stability of viscous solutions and yields a convergence result in the zero viscosity limit to smooth solutions in an l p framework it also provides a weak strong uniqueness theorem for measure valued solutions of the hyperbolic problem in the second part the relative entropy identity is developed for the systems of gas dynamics for viscous and heat conducting gases and for the system of thermoviscoelasticity both including viscosity and heat conduction effects the dissipation mechanisms and the concentration measures play different roles when applying the method to the general class of hyperbolic parabolic systems and to the specific examples and their ramifications are highlighted

structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics we consider a model of stress relaxation approximating the equations of elastodynamics necessary and sufficient conditions are derived for the model to be equipped with a global free energy and to have positive entropy production the resulting class allows for both convex and non convex equilibrium potentials for convex equilibrium potentials we prove a strong dissipation estimate and two relative energy estimates for the relative entropy of the relaxation process and the modulated relative energy both give convergence results to smooth solutions for polyconvex equilibrium potentials an augmenting of the system of polyconvex elastodynamics and the null lagrangian structure suggest an appropriate notion of relative energy we prove convergence of viscosity approximations to polyconvex elastodynamics in the regime where the limit solution remains smooth a modulated relative energy is also obtained for the polyconvex case which shows stability of relaxation approximations

revisiting the nystrom method for improved large scale machine learning we reconsider randomized algorithms for the low rank approximation of symmetric positive semi definite spsd matrices such as laplacian and kernel matrices that arise in data analysis and machine learning applications our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of spsd matrices our results highlight complementary aspects of sampling versus projection methods they characterize the effects of common data preprocessing steps on the performance of these algorithms and they point to important differences between uniform sampling and nonuniform sampling methods based on leverage scores in addition our empirical results illustrate that existing theory is so weak that it does not provide even a qualitative guide to practice thus we complement our empirical results with a suite of worst case theoretical bounds for both random sampling and random projection methods these bounds are qualitatively superior to existing bounds e g improved additive error bounds for spectral and frobenius norm error and relative error bounds for trace norm error and they point to future directions to make these algorithms useful in even larger scale machine learning applications