closed loop identification for the best asymptotic performance of adaptive robust control discrete linear systems subjected to both additive and parametric deterministic disturbances are considered the certainty equivalence principle is used for the design of adaptive control two different estimation algorithms are proposed to meet different control objectives in the regulation problem with the worst case limsup performance index

sonic hyperbolic phase transitions and chapman jouguet detonations abstract we prove that the cauchy problem for an n n system of strictly hyperbolic conservation laws in one space dimension admits a weak global solution also in presence of sonic phase boundaries applications to chapman jouguet detonations liquid vapor transitions and elastodynamics are considered

the bochner schoenberg eberlein property for commutative banach algebras especially fourier and fourier stieltjes algebras the classical bochner schoenberg eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group g which arise as fourier stieltjes transforms of elements of the measure algebra m g of g this has led to the study of the algebra of bse functions on the spectrum of an arbitrary commutative banach algebra and of the concept of a bse algebra as introduced by takahasi and hatori since then bse algebras have been studied by several authors in this paper we investigate bse algebras in the general context on the one hand and on the other hand we specialize to fourier and fourier stieltjes algebras of locally compact groups

improved stability robustness bounds using state transformation for linear discrete systems abstract sufficient condition bounds on the linear time varying perturbations for robust stability of an asymptotically stable linear time invariant discrete time system have been reported recently the development involves both schwartz and triangular inequalities and tends to give conservative results this paper uses state transformation to obtain improvement in these bounds both unstructured and structured perturbation bounds are shown to improve using transformations the proposed analysis is applied to a fourth order macroeconomic system model

regularity and large time behaviour of solutions of a conservation law without convexity a l aide de la methode des caracteristiques generalisees on etudie la regularite et le comportement a grand des solutions faibles admissibles d une seule loi de conservation a 1 variable d espace avec un point d inflexion

global existence for systems of parabolic conservation laws in several space variables abstract we prove the global existence of solutions of the cauchy problem for certain systems of conservation laws with artificial viscosity terms added the system is assumed to admit a quadratic entropy which is consistent with the viscosity matrix and the initial data is assumed to be close to a constant in l2 l in particular our result applies to the equations of compressible fluid flow in two and three space variables

computer aided determination of stability robustness measure of linear discrete time systems abstract in this paper several upper bounds for parameter variations of a linear discrete time system that is expressed in either matrix or polynomial form are presented within these upper bounds the system remains asymptotically stable these upper bounds which are only a set of sufficient conditions are then used iteratively in a computer aided algorithm to reach to the largest numerical such upper bounds the largest numerical upper bound is called the stability robustness measure of the discrete time dynamic system

on the maximal smoothing effect for multidimensional scalar conservation laws abstract in 1994 lions perthame and tadmor conjectured an optimal smoothing effect for entropy solutions of multidimensional scalar conservation laws this effect estimated in fractional sobolev spaces is linked to the flux nonlinearity we use a new definition of a nonlinear smooth flux in order to show that the conjectured smoothing effect cannot be exceeded first one dimensional solutions are considered in fractional b v spaces then the multidimensional case is handled with a monophase solution

smoothing effect in bvφ for entropy solutions of scalar conservation laws abstract this paper deals with a sharp smoothing effect for entropy solutions of one dimensional scalar conservation laws with a degenerate convex flux we briefly explain why degenerate fluxes are related with the optimal smoothing effect conjectured by lions perthame tadmor for entropy solutions of multidimensional conservation laws it turns out that generalized spaces of bounded variation b v are particularly suitable better than sobolev spaces to quantify the regularizing effect and to obtain traces as in bv the function in question is linked to the degeneracy of the flux up to the present the lax ole nik formula has provided optimal results for a uniformly convex flux this formula is validated in this paper for the more general class of c 1 strictly convex fluxes which contains degenerate convex fluxes and enables the b v smoothing effect in this class we give a complete proof that for a c 1 strictly convex flux the lax ole nik formula provides the unique entropy solution namely the kruzhkov solution

formation of diffusion waves in a scalar conservation law with convection we study the scalar conservation law ut c x u x b u2 x uxx c 0 which is a model equation for the behavior of weak transverse waves near a viscous transitional shock solutions are shown to decay in l to a pair of diffusion waves moving apart at speeds c oo and c oo behavior that has been observed numerically in solutions of the full equations the interesting aspect of the analysis is that the asymptotic state of the solution is not known a priori in contrast to cases treated previously

adaptive stabilization of time varying discrete time linear systems we develop an adaptive control technique for the regulation of a class of linear discrete time time varying system the only a priori knowledge required is a bound of the varying component of the parameters the result is concerned with global behaviour

nonlinear stability of an undercompressive shock for complex burgers equation though there is strong numerical evidence for the stability of undercompressive shocks their stability has not been verified analytically in particular the energy methods used to analyze stability of standard shocks do not apply here we present the first proof of stability for a particular undercompresive shock the real burgers shock considered as a solution of the complex burgers equation our analysis is by direct calculation of the green s function for the linearized equations combined with pointwise estimates of nonlinear effects a benefit of this method is to obtain fairly detailed information about the solution includingl1 behavior and rates of decay in different regions of space

how parabolic free boundaries approximate hyperbolic fronts a rather complete study of the existence and qualitative behaviour of the boundaries of the support of solutions of the cauchy problem for nonlinear first order and second order scalar conservation laws is presented among other properties it is shown that under appropriate assumptions parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

improved measures of stability robustness for linear state space models in this paper the aspect of stability robustness of linear systems is analyzed in the time domain a bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a lyapunov matrix equation solution the resulting bound is shown to be an improved bound over the ones recently reported in the literature also special cases of the nominal system matrix are considered for which the bound is given in terms of the nominal matrix thereby avoiding the solution of the lyapunov matrix equation examples given include comparison of the proposed approach with the recently reported results

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis

on nonlinear stability of general undercompressive viscous shock waves we study the nonlinear stability of general undercompressive viscous shock waves previously the authors showed stability in a special case when the shock phase shift can be determined a priori from the total mass of the perturbation using new pointwise methods by examining time invariants associated with the linearized equations we can now overcome a new difficulty in the general case namely nonlinear movement of the shock we introduce a coordinate transformation suitable to treat this new aspect and demonstrate our method by analyzing a model system of generic type we obtain sharp pointwise bounds andlp behavior of the solution for allp 1 p

large time behavior for conservation laws with source in a bounded domain here u u x t u r precise assumptions will be given later we are in particular interested in the asymptotic behavior of solutions to problem 1 3 equation of the form 1 is called reaction convection equation or balance law the correct setting to deal with for such equations is the one given by entropy solutions in the sense of kruz kov in 15 in such class it is well known that the cauchy problem has a unique solution continuously depending on initial data in l norm in this article we consider boundary conditions and we analyze the influence of such conditions on the whole solution as time goes on such conditions for equations of the form 1 were considered in 1 it turns out that in order to have existence uniqueness and continuous dependence conditions 3 have to be interpreted in a non classical fashion following 1 we look for entropy solutions of 1 such that their boundary values belong to appropriate sets details will be given later on article id jdeq 1999 3669 available online at http www idealibrary com on

asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to n waves abstract the goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws general convex flux f u 0 is considered with an assumption lim u 0 uf u f u 1 we show that under suitable conditions on the initial value its solution converges to an n wave in l1 norm with the optimal convergence order of o 1 t the technique we use in this article is to enclose the solution with two rarefaction waves we also show a uniform convergence order in the sense of graphs a numerical example of this phenomenon is included

an oleinik type estimate for a convection diffusion equation and convergence to n waves in this article we propose an oleinik type estimate for sign changing solutions to a convection diffusion equation ut u x uxx u x 0 u0 x u x r 1 0 since the oleinik entropy inequality holds for nonnegative solutions or inviscid case 0 only the theoretical progress for the case was limited in this paper we show that its solution satisfies an oleinik type estimate t2 ux c 1 0 where c c u0 0 using this estimate the convergence to an n wave is proved for sign changing solutions and the theoretical gap in asymptotic convergence of the corresponding problem is filled

non classical riemann solvers with nucleation we introduce a new nonclassical riemann solver for scalar conservation laws with concave convex flux function this solver is based on both a kinetic relation which determines the propagation speed of undercompressive nonclassical shock waves and a nucleation crite rion which makes a choice between a classical riemann solution and a nonclassical one we establish the existence of nonclassical entropy solutions of the cauchy problem and discuss several examples of wave interactions we also show the existence of a class of solutions called splitting merging solutions which are made of two large shocks and small bv bounded variation perturbations the nucleation solvers as we call them are applied to and actually motivated by the theory of thin film flows they help explain numerical results observed for such flows

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

optimal design of robust controllers for uncertain discrete time systems this paper presents a fast algorithm for the design of robust output feedback controllers for linear uncertain discrete time systems the algorithm utilizes a version of the broyden fletcher goldfarb shanno bfgs optimization method of conjugate directions and minimizes a performance index that includes a linear quadratic regulator lqr term to optimize performance and a robustness term based on recently developed bounds the minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied the case of unstructured perturbations in a has been the only one studied in the robust controller design literature the present algorithm introduces a unified approach to both cases of unstructured and structured perturbations in the matrices of a state space model for the special case of unstructured perturbations in a only the algorithm is shown to improve considerably the existing unstructured uncertainty bound several examples including an aircraft cont

n waves in elasticity we study the large time behavior of solutions of the one dimensional equations of elasticity typically a nonconvex system of conservation laws we show that solutions with compact initial support converge in l1 to a superposition of n waves at algebraic rate likewise we show that the perturbation expansion of weakly nonlinear geometric optics is uniformly valid to second order our analysis uses approximate scalar laws together with l1 stability of scalar solutions and decay in total variation of the wave speed

robust stability bounds on time varying perturbations for state space models of linear discrete time systems the stability robustness of linear discrete time systems in the time domain is addressed using the lyapunov approach bounds on linear time varying perturbations that maintain the stability of an asymptotically stable linear time invariant discrete time nominal system are obtained for both structured and unstructured independent perturbations bounds are also derived assuming that various elements of the system matrix are perturbed dependently the result for the structured perturbation case is extended to the stability analysis of interval matrices

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

asymptotic behavior of solutions of a conservation law without convexity conditions in this paper we study the asymptotic behavior for the hyperbolic conservation law u i 0 t 0 oo x co 1 1 u x 0 uo x al x co 1 2 with riemann like data for x large the function f is a smooth nonlinear function of u in general eq 1 1 does not have a continuous solution for all time shock curves appear after finite time we will consider a piecewise continuous weak solution of 1 1 19 lo it is well known that across a discontinuity line x x t the solution satisfies the rankine hugoniot condifion r h and the entropy condition e 111

source solutions and asymptotic behavior in conservation laws abstract we study the uniqueness of the solutions to the scalar conservation law u t u x 0 when the initial datum is a finite measure the case of a dirac mass is particularly emphasized it is shown how it provides a description of the asymptotic behavior of the solutions initiated by an arbitrary integrable function this behavior is proved to depend on one parameter in the case when is odd while it depends on two when is convex

a note on the riemann problem for general n n conservation laws we analyze the structure of the general solution of the riemann problem for a strictly hyperbolic system of conservation laws whose characteristic fields are neither genuinely non linear nor linearly degenerate in the sense of lax

characterisations of fourier and fourier stieltjes algebras on locally compact groups abstract motivated by the beautiful work of m a rieffel 1965 and of m e walter 1974 we obtain characterisations of the fourier algebra a g of a locally compact group g in terms of the class of f algebras i e a banach algebra a such that its dual a is a w algebra whose identity is multiplicative on a for example we show that the fourier algebras are precisely those commutative semisimple f algebras that are tauberian contain a nonzero real element and possess a dual semigroup that acts transitively on their spectrums our characterisations fall into three flavours where the first one will be the basis of the other two the first flavour also implies a simple characterisation of when the predual of a hopf von neumann algebra is the fourier algebra of a locally compact group we also obtain similar characterisations of the fourier stieltjes algebras of g en route we prove some new results on the problem of when a subalgebra of a g is the whole algebra and on representations of discrete groups

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

a note on robust stability bounds the authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of lyapunov functions results obtained with quadratic and with vector lyapunov functions are compared simple examples are used to illustrate the effects of the choice of functions corresponding majorizations and system decompositions

a conservation law with point source and discontinuous flux function modelling continuous sedimentation continuous sedimentation of solid particles in a liquid takes place in a clarifier thickener unit which has one feed inlet and two outlets the aim of the paper is to formulate and analyse a dynamic model for this process under idealized physical conditions the conservation of mass yields the scalar conservation law frac partial u x t partial t frac partial partial x f u x t x s t delta x where delta is the dirac measure s is a source and f is a flux function which is discontinuous at three points in the one dimensional space coordinate x under certain regularity assumptions a procedure for constructing a solution locally in time is presented the nonlinear phenomena are complicated and so is the general construction of a solution the problem of nonuniqueness due to the discontinuities of f u cdot is handled by a generalized entropy condition an advantage of this approach is that the a priori boundary conditions at the discontinuities

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

adjoint and compensated compactness methods for hamilton jacobi pde we investigate the vanishing viscosity limit for hamilton jacobi pde with nonconvex hamiltonians and present a new method to augment the standard viscosity solution approach the main idea is to introduce a solution e of the adjoint of the formal linearization and then to integrate by parts with respect to the density e this procedure leads to a natural phase space kinetic formulation and also to a new compensated compactness technique

new robust stability bounds of linear discrete time systems with time varying uncertainties this paper presents new uncertain parameter variation bounds for linear discrete time systems to preserve asymptotic stability the lyapunov method is utilized to treat both structured and unstructured uncertainties and the results are optimized with respect to a parameter in the inequality used when applied to examples considered by previous authors our results give less conservative bounds