some new simple stability criteria of linear neutral systems with a single delay this article mainly considers the linear neutral delay differential systems with a single delay using the characteristic equation of the system new simple delay independent asymptotic and exponential stability criteria are derived in terms of the matrix measure the spectral norm and the spectral radius of the corresponding matrices numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results l m li stability of linear neutral delay differential systems bull aust math soc 38 1988 339 344 g d hu g d hu some simple criteria for stability of neutral delay differential systems appl math comput 80 1996 257 271 d q cao ping he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu b cahlon algebraic criteria for stability of linear neutral systems with a single delay j comput appl math 135 2001 125 130

on stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls abstract the paper discusses stabilizing effects of some time delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations first we derive explicit delay dependent stability conditions that are applicable to a family of time delayed systems with simultaneously triangularizable system matrices then using this criterion and other argumentation we employ diagonal delayed feedback controls of conventional and pyragas type to stabilize unstable steady states of the studied autonomous system more precisely we formulate explicit non improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization as an illustration we stabilize the unstable steady states of the rossler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior also we consider a non diagonal feedback control whose rotational gain matrix involving a feedback strength and phase commutes with the jacobi matrix of the uncontrolled system and show its larger stabilization potential with respect to the appropriate diagonal control the obtained results are tested by numerical experiments and confronted with the existing results as a supplement we provide matlab codes supporting theoretical conclusions

stability criteria of linear neutral systems with multiple delays in the present note stability of linear neutral systems with multiple delays is investigated by principle of the argument stability criteria are derived which are necessary and sufficient for asymptotic stability of the neutral systems the stability criteria need only to evaluate the characteristic function and the argument on the boundary of a certain rectangular region several numerical examples are given to illustrate the results

novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations in this paper a class of neutral systems with mixed delays and nonlinear perturbations is considered a novel robust stability criterion of the system is derived by using lyapunov method the criterion can be easily solved by efficient convex optimization algorithms some numerical examples are given to illustrate our result

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

on stability of systems of delay differential equations abstract in this paper we give necessary and sufficient conditions for the asymptotic stability of the zero solution of the system of linear delay differential equations of the form x t ax t 1 ax t where a is an n n matrix 0 is constant and 0 1 we reduce this to systems of first and second order problems our stability results are given in terms of the eigenvalues of a the proof of our results are carried out by an application of pontryagin s criterion for quasi polynomials to the characteristic functions of subsystems of the delay differential equations we also provide four algorithmic stability tests and include several examples

easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems this paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems and establishes the relationship between the eigenvalue distribution and delay independent stability of neutral differential systems by using the complete discrimination system for polynomials easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems are established the algebraic criteria generalize and unify the relevant results in the literature moreover the maximal delay bound guaranteeing stability can be determined if the systems are not delay independent stable some numerical examples are provided to illustrate the effectiveness of our results c 2007 elsevier b v all rights reserved

hopf bifurcation of viscous shock waves in compressible gas dynamics and mhd extending our previous results for artificial viscosity systems we show under suitable spectral hypotheses that shock wave solutions of compressible navier stokes and magnetohydrodynamics equations undergo hopf bifurcation to nearby time periodic solutions the main new difficulty associated with physical viscosity and the corresponding absence of parabolic smoothing is the need to show that the difference between nonlinear and linearized solution operators is quadratically small in h s for data in h s we accomplish this by a novel energy estimate carried out in lagrangian coordinates interestingly this estimate is false in eulerian coordinates at the same time we greatly sharpen and simplify the analysis of the previous work

the existence of current vortex sheets in ideal compressible magnetohydrodynamics we prove the local in time existence of solutions with a surface of current vortex sheet tangential discontinuity of the equations of ideal compressible magnetohydrodynamics in three space dimensions provided that a stability condition is satisfied at each point of the initial discontinuity this paper is a natural completion of our previous analysis trakhinin in arch ration mech anal 177 331 366 2005 where a sufficient condition for the weak stability of planar current vortex sheets was found and a basic a priori estimate was proved for the linearized variable coefficients problem for nonplanar discontinuities the original nonlinear problem is a free boundary hyperbolic problem since the free boundary is characteristic the functional setting is provided by the anisotropic weighted sobolev spaces h m the fact that the kreiss lopatinski condition is satisfied only in a weak sense yields losses of derivatives in a priori estimates therefore we prove our existence theorem by a suitable nash moser type iteration scheme

discretized lyapunov functional for systems with distributed delay and piecewise constant coefficients the stability problem for systems with distributed delay is considered using discretized lyapunov functional the coefficients associated with the distributed delay are assumed to be piecewise constant and the discretization mesh may be non uniform the resulting stability criteria are written in the form of linear matrix inequality numerical examples are also provided to illustrate the effectiveness of the method the basic idea can be extended to a more general setting with more involved formulation

asymptotic stability of neutral differential systems with many delays we are concerned with delay independent asymptotic stability of linear system of neutral differential equations we first establish a sufficient and necessary condition for the system to be delay independently asymptotically stable and then give some equivalent stability conditions this paper improves many recent results on the asymptotic stability in the literature one example is given to show that the sufficient and necessary condition is easy to verify

on the design of observer based controller of linear neutral delay differential systems in this note the observer based control problem for a class of linear delay differential systems of neutral type is investigated using the lyapunov method a criterion for asymptotic stability is derived in terms of matrix inequalities which solved by convex optimization algorithms a numerical example is given to illustrate the proposed method

lmi approach to robust h filtering for neutral delay differential systems in this paper we investigate the problems of stability and h filtering for a class of linear neutral delay differential systems a linear matrix inequality approach is proposed to design a robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example illustrate the theoretical results

stability of discrete delay systems boundary criteria this paper deals with the stability of linear discrete delay systems two stability criteria that are described by evaluating a corresponding harmonic function on the boundary of a torus region are presented testing these criteria can be proved to be much easier than those reported in the literature

convex entropy hopf bifurcation and viscous and inviscid shock stability we consider by a combination of analytical and numerical techniques some basic questions regarding the relations between inviscid and viscous stability and the existence of a convex entropy specifically for a system possessing a convex entropy in particular for the equations of gas dynamics with a convex equation of state we ask 1 can inviscid instability occur 2 can viscous instability not detected by inviscid theory occur 3 can there occur the necessarily viscous effect of hopf bifurcation or galloping instability and perhaps most important from a practical point of view 4 as shock amplitude is increased from the stable weak amplitude limit can there occur a first transition from viscous stability to instability that is not detected by inviscid theory we show that 1 does occur for strictly hyperbolic genuinely nonlinear gas dynamics with certain convex equations of state while 2 and 3 do occur for an artifically constructed system with convex viscosity compatible entropy we do not know of an example for which 4 occurs leaving this as a key open question in viscous shock theory related to the principal eigenvalue property of sturm liouville and related operators in analogy with and partly proceeding close to the analysis of smith on non uniqueness of the riemann problem we obtain convenient criteria for shock in stability in the form of necessary and sufficient conditions on the equation of state

asymptotic stability for the system of neutral delay differential equations abstract this paper deals with the asymptotic stability of the system of neutral delay differential equations in an angle which has fewer reports stability regions are presented geometrically as well as two criteria which are obtained through the evaluation of a harmonic function on the boundary of a certain region numerical experiments on various circumstances are shown to locate the specific region which can make the system unstable so as to exclude it from the whole complex plane

existence of compressible current vortex sheets variable coefficients linear analysis we study the initial boundary value problem resulting from the linearization of the equations of ideal compressible magnetohydrodynamics and the rankine hugoniot relations about an unsteady piecewise smooth solution this solution is supposed to be a classical solution of the system of magnetohydrodynamics on either side of a surface of tangential discontinuity current vortex sheet under some assumptions on the unperturbed flow we prove an energy a priori estimate for the linearized problem since the tangential discontinuity is characteristic the functional setting is provided by the anisotropic weighted sobolev space w21 despite the fact that the constant coefficients linearized problem does not meet the uniform kreiss lopatinskii condition the estimate we obtain is without loss of smoothness even for the variable coefficients problem and nonplanar current vortex sheets the result of this paper is a necessary step in proving the local in time existence of current vortex sheet solutions of the nonlinear equations of magnetohydrodynamics

delay independent stability criteria for discrete delay systems several sufficient conditions for stability of linear discrete delay systems are derived since these conditions are independent of the delay and possess simple forms they will provide useful tools to check stability of the systems at the first stage

stability of retarded delay differential systems a practical stability test for linear retarded delay differential systems is proposed based on the fact that all unstable zeros of the characteristic quasipolynomial must lie within a restricted bounded region of the complex plane the test provides a readily computable necessary and sufficient condition for asymptotic stability it also copes equally well with both cases of commensurate and non commensurate delays furthermore a method for evaluating the abscissa of stability of the quasi polynomial defined as the largest of the real parts of the zeros of the quasipolynomial is given the method is based on a known technique which makes repeated use of a stability test and thereby avoids the calculation of all the zeros the stability test and the method for computing the abscissa of stability provide useful computational tools for the design of dynamical systems with delays using the method of inequalities numerical examples are given

on robust stabilization for neutral delay differential systems with parametric uncertainties and its application this paper considers the problem of robust stabilization for uncertain neutral delay differential systems based on the lyapunov method a delay dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms then the method presented is extended to systems with controller gain variations that is the design problem for the nonfragile controller is considered a numerical example is included to illustrate the design procedure of the proposed method

limit linear series basic theory in this paper we introduce techniques for handling the degeneration of linear series on smooth curves as the curves degenerate to a certain type of reducible curves curves of compact type the technically much simpler special case of 1 dimensional series was developed by beauville 2 knudsen 21 23 harris and mumford 17 in the guise of admissible covers it has proved very useful for studying the moduli space of curves the above papers and harris 16 and the simplest sorts of weierstrass points diaz 4 with our extended tools we are able to prove for example that in this paper we present the basic theory of limit linear series necessary for proving these results the results themselves will be taken up in our forthcoming papers 8 12 simpler applications not requiring the tools developed in this paper but perhaps clarified by them have already been given in our papers 5 7

on asymptotic stability of delay difference systems in this paper we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay difference systems by using a discrete version of the second lyapunov method our results can be well suited for computational purposes

emergence of unstable modes for classical shock waves in isothermal ideal mhd abstract this note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity for this mathematically prototypical material it identifies mainly numerically two critical manifolds in parameter space across which slow resp fast mhd shock waves undergo emergence of a complex conjugate pair of unstable transverse modes for slow shocks this emergence occurs in a particularly interesting way already in the parallel case in which it happens at the spectral value 0 and the critical manifold possesses a simple explicit algebraic representation results of refined numerical treatment show that within the set of non parallel slow shocks the unstable mode pair emerges from two generically different spectral values i for fast shocks the critical manifold does not intersect the parallel regime and the emergence within the set of non parallel fast shocks again starts from two generically different spectral values

delay independent exponential stability criteria for time varying discrete delay systems derives delay independent exponential stability conditions for linear nonlinear time varying discrete delay systems since these conditions are of delay independence and easily verifiable they may provide handy tools for the stability analysis

the refined inviscid stability condition and cellular instability of viscous shock waves abstract combining the work of serre and zumbrun benzoni gavage serre and zumbrun and texier and zumbrun we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite cross section duct the violation of the refined planar stability condition of zumbrun serre a viscous correction of the inviscid planar stability condition of majda more precisely we show for a model problem involving flow in a rectangular duct with artificial periodic boundary conditions that transition to multidimensional instability through violation of the refined stability condition of planar viscous shock waves on the whole space generically implies for a duct of sufficiently large cross section a cascade of hopf bifurcations involving more and more complicated cellular instabilities the refined condition is numerically calculable as described by benzoni gavage serre zumbrun

asymptotic and numerical stability of systems of neutral differential equations with many delays we are concerned with the asymptotic stability of a system of linear neutral differential equations with many delays in the form y t ly t email protected i 1dm iy email protected i email protected i 1dn iy email protected i where l m i n email protected c n x n i 1 2 d are constant complex matrices t i 0 i 1 2 d are constant delays and y t y 1 t y 2 t y n t t is an unknown vector valued function for t 0 we first establish a new result for the distribution of the roots of its characteristic function next we obtain a sufficient condition for its asymptotic stability and then we investigate the corresponding numerical stability of linear multistep methods applied to such systems one numerical example is given to testify our numerical analysis

generic types and transitions in hyperbolic initial boundary value problems the stability of linear initial boundary value problems for hyperbolic systems with constant coefficients is linked to the zeros of the so called lopatinskii determinant depending on the location of these zeros problems may be either unstable strongly stable or weakly stable the first two classes are known to be open in the sense that the instability or the strong stability persists under a small change of coefficients in the differential operator and or in the boundary condition here we show that a third open class exists which we call weakly stable of real type many examples of physical or mathematical interest depend on one or more parameters and the determination of the stability class as a function of these parameters usually needs an involved computation we simplify it by characterizing the transitions from one open class to another one these boundaries are easier to determine since they must solve some overdetermined algebraic system applications to the wave equation linear elasticity shock waves and phase boundaries in fluid mechanics are given

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

some sufficient conditions for exponential stability of linear neutral functional differential equations abstract in this paper we give some sufficient conditions for exponential stability of linear neutral functional differential equations the obtained results are extensions of the recent results in d q cao p he stability criteria of linear neutral systems with a single delay appl math comput 148 2004 135 143 d q cao p he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu x f zou stability of linear neutral systems with multiple delays boundary criteria appl math comput 148 2004 707 715 j h park s won a note on stability of neutral delay differential systems j franklin inst 336 1999 1 9 to linear neutral functional differential equations

on robust h filter design for uncertain neural systems lmi optimization approach this article deals with the robust h filtering problem for neutral delay differential systems with parametric uncertainties a linear matrix inequality lmi approach is proposed to design the robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example is provided to illustrate the validity of proposed design approach

numerical stability of the t methods for systems of differential equations with several delay terms abstract consider the following two dimensional delay differential equation dde u t a 1 u t b 1 v t d 2 v t a 2 v t b 2 u t d 1 t t 0 with the initial conditions u t u 0 t t 0 d 1 t t 0 v t v 0 t t 0 d 2 t t 0 where a j b j c d j 0 and u 0 t 0 t are continuous and complex valued the author give the sufficient conditions for the asymptotic stability of equation 0 1 the numerical stabilities of the linear method and the one leg method are investigated by analysing their stabilities behaviour in the solutions of 0 1 it is shown that the linear method is gp stable if and only if 1 2 1 and that the one leg method is gp stable if and only if 1

structural stability of shock waves in 2d compressible elastodynamics we study the two dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local in time existence and uniqueness of discontinuous shock front solutions of the equations of compressible elastodynamics in two space dimensions by the energy method based on a symmetrization of the wave equation and giving an a priori estimate without loss of derivatives for solutions of the constant coefficients linearized problem we find a condition sufficient for the uniform stability of rectilinear shock waves comparing this condition with that for the uniform stability of shock waves in isentropic gas dynamics we make the conclusion that the elastic force plays stabilizing role in particular we show that as in isentropic gas dynamics all compressive shock waves are uniformly stable for convex equations of state moreover for some particular deformations and general equations of state by the direct test of the uniform kreiss lopatinski condition we show that the stability condition found by the energy method is not only sufficient but also necessary for uniform stability as is known uniform stability implies structural stability of corresponding curved shock waves

stability of neutral delay differential systems boundary criteria this paper deals with the delay dependent stability of linear invariant neutral delay differential systems with a positive constant delay six criteria that are described by evaluating a corresponding harmonic function on the boundary of a certain rectangular region are presented

simple stability criteria for nonlinear time varying discrete systems abstract we present two sufficient conditions for asymptotic stability of nonlinear time varying discrete systems our main results generalize mori s result for linear discrete time invariant systems to nonlinear time varying systems

on guaranteed cost control of neutral systems by retarded integral state feedback in this paper the guaranteed cost control problem for a class of neutral delay differential systems with a given quadratic cost functions is investigated the problem is to design a memory state feedback controller such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound some criteria for the existence of such controllers is derived based on the linear matrix inequality lmi approach combined with the lyapunov method a parameterized characterization of the controllers is given in terms of the feasible solutions to the certain lmis a numerical example is given to illustrate the proposed method

on computing the maximum time delay bound for stability of linear neutral systems this note is concerned with the stability problem of linear delay differential systems of neutral type a discretized lyapunov functional approach is developed the resulting stability criterion is formulated in the form of a linear matrix inequality for nominal systems the analytical results can be approached with fine discretization numerical examples show significant improvement over approaches in the literature

algebraic criteria for stability of linear neutral systems with a single delay abstract the stability of linear neutral delay differential systems with a single delay via routh hurwitz and schur cohn criteria is investigated some algebraic criteria for delay independent stability are presented these criteria may complement those reported in the literature finally two examples illustrate the criteria

a complete 2d stability analysis of fast mhd shocks in an ideal gas an algorithm of numerical testing of the uniform lopatinski condition for linearized stability problems for 1 shocks is suggested the algorithm is used for finding the domains of uniform stability neutral stability and instability of planar fast mhd shocks a complete stability analysis of fast mhd shock waves is first carried out in two space dimensions for the case of an ideal gas main results are given for the adiabatic constant 5 3 mono atomic gas that is most natural for the mhd model the cases 7 5 two atomic gas and 5 3 are briefly discussed not only the domains of instability and linear in the usual sense stability but also the domains of uniform stability for which a corresponding linearized stability problem satisfies the uniform lopatinski condition are numerically found for different given angles of inclination of the magnetic field behind the shock to the planar shock front as is known uniform linearized stability implies the nonlinear stability that is local existence of discontinuous shock front solutions of a quasilinear system of hyperbolic conservation laws

stability of linear neutral systems with multiple delays boundary criteria the stability of linear neutral delay differential systems with multiple delays is investigated the delay dependent stability criteria are presented through the evaluation of the corresponding harmonic functions on the boundary of a certain half circular region and such criteria are extensions of some results in literature an example is given to illustrate the stability criteria

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

computable stability criterion of linear neutral systems with unstable difference operators abstract this paper is concerned with linear neutral systems with unstable difference operators all the unstable characteristic roots of the linear neutral systems are located in a bounded half circular region then based on the argument principle a computable stability criterion is derived which is necessary and sufficient for asymptotic stability of the neutral systems furthermore the number of the unstable characteristic roots is given the main results of the present paper extend those in literature numerical experiments are provided to illustrate the main results

on delay dependent robust stability of uncertain neutral systems with interval time varying delays in this paper the problem of a new delay dependent robust stability criterion for neutral systems is investigated the considered system has time varying structured uncertainties and interval time varying delays based on the lyapunov method a delay dependent criterion for asymptotic stability is established in terms of lmi linear matrix inequality numerical examples are carried out to support the effectiveness of our results

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

the numerical solution of discrete delay systems in this note we consider the numerical solution of initial value discrete delay systems an interpolation procedure is introduced to compute the numerical solution the convergence and stability of the interpolation procedure for the discrete delay systems is discussed

the geometry of the moduli space of curves of genus 23 the problem of describing the birational geometry of the moduli space mg of complex curves of genus g has a long history severi already knew in 1915 thatmg is unirational for g 10 cf sev see also ac1 for a modern proof in the same paper severi conjectured thatmg is unirational for all genera g then for a long period this problem seemed intractable mumford writes in mu p 51 whether more mg s g 11 are unirational or not is a very interesting problem but one which looks very hard too especially if g is quite large the breakthrough came in the eighties when eisenbud harris and mumford proved that mg is of general type as soon as g 24 and that the kodaira dimension of m23 is 1 see hm eh3 we note that mg is rational for g 6 see dol for problems concerning the rationality of various moduli spaces severi s proof of the unirationality of mg for small g was based on representing a general curve of genus g as a plane curve of degree d with nodes this is possible when d 2g 3 2 when the number of nodes is small i e d 1 d 2 6 the dominant map from the variety of plane curves of degree d and genus g to mg yields a rational parametrization of the moduli space the two conditions involving d and can be satisfied only when g 10 so severi s argument cannot be extended for other genera however using much more subtle ideas chang ran and sernesi proved the unirationality of mg for g 11 12 13 see cr1 se1 while for g 15 16 they proved that the kodaira dimension is see cr2 4 the remaining cases g 14 and 17 g 23 are still quite mysterious harris and morrison conjectured in hmo that mg is uniruled precisely when g 23 all these facts indicate that m23 is a very interesting transition case our main result is the following

lyapunov equation for the stability of linear delay systems of retarded and neutral type in this note the delay independent stability of delay systems is studied it is shown that the strong delay independent stability is equivalent to the feasibility of certain linear matrix inequality lmi that is to the existence of a quadratic lyapunov krasovskii functional independent of the nonnegative value of the delay this constitutes the analogue of some well known properties of finite dimensional systems this result is then applied to study delay independent stability of systems with polytopic uncertainties

on the existence of certain families of curves introduction 25 w 1 generalities on families of curves in ip 28 w the map 0 d 33 w 3 the number of moduli of a family 40 w 4 plane curves existence of families with the expected number of moduli 43 w 5 smoothing certain reducible curves in ip r r 3 47 w 6 curves in ip r 3 existence of families with the expected number of moduli 52 w curves in ip3 a more general existence theorem 55

the numerical solution of discrete delay systems abstract in this note we consider the numerical solution of initial value discrete delay systems an interpolation procedure is introduced to compute the numerical solution the stability of the interpolation procedure for linear discrete delay systems is discussed

a new simple approach to the derivation of exact analytical formulae for the zeros of analytic functions a very simple method for the construction of the polynomial whose zeros coincide with the zeros of an analytic function inside and along a simple closed contour in the complex plane based on an appropriate application of the cauchy theorem in complex analysis is proposed the present method was motivated by the classical burniston siewert method based on the theory of the riemann hilbert boundary value problem for the construction of the aforementioned polynomial but although essentially equivalent to the burniston siewert method it is much simpler

galloping instability of viscous shock waves abstract motivated by physical and numerical observations of time oscillatory galloping spinning and cellular instabilities of detonation waves we study poincare hopf bifurcation of traveling wave solutions of viscous conservation laws the main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum preventing standard reduction to a finite dimensional center manifold we overcome this by direct lyapunov schmidt reduction using detailed pointwise bounds on the linearized solution operator to carry out a nonstandard implicit function construction in the absence of a spectral gap the key computation is a space time stability estimate on the transverse linearized solution operator reminiscent of duhamel estimates carried out on the full solution operator in the study of nonlinear stability of spectrally stable traveling waves

stability criteria of linear neutral systems with a single delay this article studies the asymptotic stability of linear neutral delay differential systems using the characteristic equation of the system new simple delay independent stability criteria are derived in terms of the spectral radius of modulus matrices numerical examples are given to demonstrate the validity of our main criteria

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

stability analysis for delay differential equations with multidelays and numerical examples in this paper we are concerned with the asymptotic stability of the delay differential equation x t a 0 x t a k x t k where a 0 a k c d d are constant complex matrices and x t k x 1 t k1 x 2 t k2 x d t kd t kl 0 stand for n x d constant delays k 1 n i 1 d we obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region we also get similar results for the neutral delay differential equation x t lx t m i x t i n j x t j where l m i and nj e c d d are constant complex matrices and i j 0 stands for constant delays i 1 m j 1 n numerical examples on various circumstances are shown to check our results which are more general than those already reported

well posedness of the linearized problem for mhd contact discontinuities abstract we study the free boundary problem for contact discontinuities in ideal compressible magnetohydrodynamics mhd they are characteristic discontinuities with no flow across the discontinuity for which the pressure the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump under the rayleigh taylor sign condition p n 0 on the jump of the normal derivative of the pressure satisfied at each point of the unperturbed contact discontinuity we prove the well posedness in sobolev spaces of the linearized problem for 2d planar mhd flows

one dimensional stability of parallel shock layers in isentropic magnetohydrodynamics abstract extending investigations of barker humpherys lafitte rudd and zumbrun for compressible gas dynamics and freistuhler and trakhinin for compressible magnetohydrodynamics we study by a combination of asymptotic ode estimates and numerical evans function computations the one dimensional stability of parallel isentropic magnetohydrodynamic shock layers over the full range of physical parameters shock amplitude strength of imposed magnetic field viscosity magnetic permeability and electrical resistivity for a law gas with 1 3 other values may be treated similarly but were not checked numerically depending on magnetic field strength these shocks may be of fast lax intermediate overcompressive or slow lax type however the shock layer is independent of magnetic field consisting of a purely gas dynamical profile in each case our results indicate stability interesting features of the analysis are the need to renormalize the evans function in order to pass continuously across parameter values where the shock changes type or toward the large amplitude limit at frequency 0 and the systematic use of winding number computations on riemann surfaces

guaranteed cost stabilization of neutral differential systems with parametric uncertainty in this paper we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function the parametric uncertainties are real time varying norm bounded and state delay is a constant the problem is to design the state feedback control laws such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and delay two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the lyapunov method the developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities

brief a practical method for analyzing the stability of neutral type lti time delayed systems a new paradigm is presented for assessing the stability posture of a general class of linear time invariant neutral time delayed systems lti ntds the ensuing method which we name the direct method dm offers several unique features it returns the number of unstable characteristic roots of the system in an explicit and non sequentially evaluated function of time delay t consequently the direct method creates exclusively all possible stability intervals of t furthermore it is shown that this method inherently verifies a widely accepted necessary condition for the t stabilizability of a lti ntds in the core of the dm lie a root clustering paradigm and the strength of rekasius transformation in mapping a transcendental characteristic equation into an equivalent rational polynomial in addition we also demonstrate by an example that dm can tackle systems with unstable starting posture for t 0 only to stabilize for higher values of delay which is rather unique in the literature

technical communique robust stability of uncertain delay differential systems of neutral type this paper focuses on the stability problem for neutral delay differential systems with norm bounded and possibly time varying uncertainty the time delay is assumed constant and known a stability criterion that is formulated in a linear matrix inequality lmi form is derived numerical examples show that the results obtained by this new criterion significantly improve the estimate of stability limit over some existing results in the literature

stability criteria for differential algebraic equations with multiple delays and their numerical solutions abstract this paper is concerned with the asymptotic stability of differential algebraic equations with multiple delays and their numerical solutions first we give a sufficient condition for delay independent stability after characterizing the coefficient matrices that satisfy this stability condition we propose some practical checkable criteria for asymptotic stability then we investigate the stability of numerical solutions obtained by methods and bdf methods finally solvability and stability of a class of weakly regular delay differential algebraic equations are analyzed

on stability criteria for uncertain delay differential systems of neutral type with time varying delays in this paper we propose a new stability criterion for uncertain neutral systems the considered system has time varying structured uncertainties and time varying delay based on the lyapunov method a delay dependent criterion for asymptotic stability is derived in terms of lmi linear matrix inequality numerical examples are given to show the effectiveness of our results