on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems an application to river pollution control we employ the stability result of thowsen on a class of linear delay systems containing uncertain elements and subject to uncertain inputs to manage a simple one reach model of a river system with time delay and subject to uncertain but bounded input as well as parameter disturbances two important indices of water quality namely biochemical oxygen demand bod and dissolved oxygen do are used as state variables while controls in the form of effluent discharge rate of bod and in stream aeration rate of do are employed to steer the system to a calculable neighborhood of a desired steady state and then maintain it there

numerical methods for hyperbolic conservation laws with stiff relaxation ii higher order godunov methods a higher order godunov method is presented for hyperbolic systems of conservation laws with stiff relaxing source terms the goal is to develop a godunov method that produces higher order accurate

the block numerical range of matrix polynomials block numerical ranges of matrix polynomials especially the quadratic numerical range are considered the main results concern spectral inclusion boundedness of the block numerical range an estimate of the resolvent in terms of the quadratic numerical range geometrical properties of the quadratic numerical range and inclusion between block numerical ranges of the matrix polynomials for refined block decompositions as an application we connect the quadratic numerical range with the localization of the spectrum of matrix polynomials

the routh hurwitz method for stability determination of linear differential difference systems abstract the characteristic quasipolynomial for a linear differential difference system is replaced by a regular polynomial to which standard stability tests for finite dimensional systems can be applied the routh hurwitz stability test is then used to determine necessary and sufficient conditions for asymptotic stability of time delay systems independent of the length of the delay

further results on stability of xd t ax t bx t t abstract our aim in this communication is to improve the existing results concerning the stability of x dot t ax t bx t it is shown that the unstable characteristic roots could be more accurately located in a bounded and restrictive region of the complex plane an iterative scheme is presented for numerical implementation of the results numerical computations are presented for illustration and comparison with previous results

stability conditions for a class of delay differential systems in this paper necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained the stability conditions reduce to positivity of a quartic equation conditions for the latter in explicit form are given by the authors in an earlier publication in addition sufficient conditions for stability for a general order delay differential system independent of delay are also obtained such conditions are ascertained from the fact that a sufficient condition for any algebraic equation to have no positive real roots is that all its coefficients be positive

technical communique on delay dependent stability and decay estimate for uncertain systems with time varying delay in this note for a class of linear uncertain systems with time varying delay a delay dependent robust stability criterion which can give information on the decay rate of the systems state is presented

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

stability conditions of delay differential systems sufficient conditions of asymptotic stability independent of delay of both the retarded and neutral types of delay differential systems are obtained the main results are based on the sufficient conditions under which the roots of the determinant of a given l l complex matrix polynomial lie either in the open left half plane or inside the unit circle therefore the explicit computation of the determinant polynomial is not required

error bounds for fractional step methods for conservation laws with source terms fractional step methods have been used to approximate solutions of scalar conservation laws with source terms in this paper the stability and accuracy of the basic fractional step algorithms are analyzed when these algorithms are used to compute discontinuous solutions of nonhomogeneous scalar conservation laws the authors show that time splitting methods for conservation laws with source terms always converge to the unique weak solution satisfying the entropy condition in particular it is proved that the l 1 errors in the splitting methods are bounded by o sqrt delta t where delta t is the splitting time step the l 1 convergence rate of a class of fully discrete splitting methods is also investigated

control of internally delayed plants by using only input output signals abstract control of internally delayed plants using only input output signals is considered frequency domain techniques using two variable polynomial algebra are used consistently the restriction imposed on the plant is moderate pole placement as well as exact model matching is examined in detail the control law obtained is simpler than that obtained via time domain techniques the synthesis method differs in the case when a 0 0 and the case when a 0 0 for the former case finite pole assignment and matching to a finite dimensional reference model is realizable but for the latter case it is not

stability of interval matrix polynomial in continuous and discrete cases abstract sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given these conditions are presented in terms of the positive definiteness of either an ln ln or l l hermitian and interval matrix therefore the computation of the determinant interval polynomial is avoided

numerical methods for hyperbolic conservation laws with stiff relaxation i spurious solutions the author considers the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed uniform spatial grid it is conjectured that certain a priori criteria ensure that the numerical method does not produce spurious solutions as the relaxation time vanishes one criterion is that the limits of vanishing relaxation time and vanishing viscosity commute for the viscous regularization of the hyperbolic system a second criterion is that a certain subcharacteristic condition be satisfied by the hyperbolic system this conjecture is supported with analytical and numerical results for a specific example the solution of generalized riemann problems of a model system of equations with a fractional step scheme in which godunov s method is coupled with the backward euler method similar ideas are applied to the numerical solution of stiff detonation problems

finite volume schemes for nonhomogeneous scalar conservation laws error estimate in this paper we study finite volume schemes for the nonhomogeneous scalar conservation law u t rm div f x t u q x t u with initial condition u x 0 u0 x the source term may be either stiff or nonstiff in both cases we prove error estimates between the approximate solution given by a finite volume scheme the scheme is totally explicit in the nonstiff case semi implicit in the stiff case and the entropy solution the order of these estimates is h frac 1 4 in space time l 1 norm h denotes the size of the mesh furthermore the error estimate does not depend on the stiffness of the source term in the stiff case

stability and the matrix lyapunov equation for delay differential systems abstract asymptotic stability independent of the delay of linear differential delay systems with commensurate and non commensurate delays is analysed using 2 d two dimensional and n d n dimensional state space models sufficient conditions for stability are obtained in terms of the frequency dependent 1 d one dimensional lyapunov equations 2 d and n d lyapunov equations with constant parameters are derived using the discrete positive real lemma and the continuous bounded real lemma

stability of discrete time matrix polynomials this paper derives conditions for the stability of discrete time systems that can be modeled by a vector difference equation where the variables are m spl times 1 vectors and the coefficients are m spl times m matrices stability of the system is related to the locations of the roots of the determinant of a real m spl times m matrix polynomial of nth order in this case sufficient conditions for the system to be stable are derived the conditions are imposed on the spl infin norm of two matrices constructed from the coefficient matrices and do not require the computation of the determinant polynomial the conditions are the extensions of one of the jury sufficient conditions for a scalar polynomial an example is used to illustrate the application of the sufficient conditions

stability of a matrix polynomial in discrete systems two sufficient conditions that the determinant of a nonsingular real m times m matrix polynomial of n th order has all its roots inside the unit circle have been obtained these conditions are represented in terms of rational functions of the coefficient matrices therefore these conditions do not require the computation of the determinant polynomial the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is expressed by the positive definiteness of an m times m hermitian matrix which is a function of z z leq 1 the first condition implies the second and hence is more restrictive than the second

on convergence of numerical schemes for hyperbolic conservation laws with stiff source terms we deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms we suppose that the source term is dissipative but it is not necessarily a lipschitzian function the convergence of the approximate solution towards the entropy solution is established for first and second order accurate muscl and for splitting semi implicit methods