a parameter uniform implicit difference scheme for solving time dependent burgers equations abstract a numerical study is made for solving one dimensional time dependent burgers equation with small coefficient of viscosity burgers equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows for high coefficient of viscosity a number of solution methodology exist in the literature 6 7 8 9 and 14 but for the sufficiently low coefficient of viscosity the exist solution methodology fail and a discrepancy occurs in the literature in this paper we present a numerical method based on finite difference which works nicely for both the cases i e low as well as high viscosity coefficient the method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh the quasilinearzation process is used to tackle the non linearity an extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter to illustrate the method numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

a finite element approach for solution of burgers equation in this study for the burgers equation which is used a model problem in turbulence and shock wave theory was given a finite element solution considering the numerical results obtained for different values of viscosity compared with cole s analytical solution it was seen that they were in good agreement

robust detection filter design in the presence of time varying system perturbations this paper discusses the problem of designing detection filters for a class of linear time varying systems the basic contribution of the paper is that by applying a time invariant equivalent representation of the original time varying system it is possible to construct a detection filter such that the solution of the design problem can be solved using algebraic methods and geometric concepts similar to the case of time invariant situations

further results on state estimation for neural networks of neutral type with time varying delay in this paper further result on design problem of state estimator for a class of neural networks of neutral type is presented a delay dependent linear matrix inequality lmi criterion for existence of the estimator is derived a numerical simulation is given to show the effectiveness of proposed estimator

improved results on robust exponential stability criteria for neutral type delayed neural networks abstract in this paper we investigate the problem of robust global exponential stability analysis for a class of neutral type neural networks the interval time varying delays allow for both slow and fast time varying delays the values of the time varying uncertain parameters are assumed to be bounded within given compact sets improved global exponential stability condition is derived by employing new lyapunov krasovskii functional and the integral inequality the developed nominal and robust stability criteria is delay dependent and characterized by linear matrix inequalities lmis the developed results are less conservative than previous published ones in the literature which are illustrated by representative numerical examples

analytical redundancy relations for fault detection and isolation in algebraic dynamic systems this paper extends the analytical redundancy techniques well developed for linear systems to fdi in non linear dynamic systems modeled by polynomial differential algebraic equations the residual evaluation form is developed for sensor actuator and process component faults fault detectability and isolability conditions are given and the design of robust structured residuals is addressed

quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation topological separation is investigated in the case of an uncertain time invariant matrix interconnected with an implicit linear transformation a quadratic separator independent of the uncertainty is shown to prove losslessly the closed loop well posedness several applications for lti descriptor system analysis are then given first some known results for stability and pole location of descriptor systems are demonstrated in a new way second contributions to robust stability analysis and time delay systems stability analysis are exposed these prove to be new even when compared to results for usual lti systems not in descriptor form all results are formulated as linear matrix inequalities lmis

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

brief paper robust fault detection based on observers for bilinear systems the design of a residual generator for robust fault detection in bilinear systems is considered two methods are presented the first one is based on a linear time invariant observer up to output injection while the second one relies on a so called kalman like observer it is shown via examples that the approach based on a kalman like observer allows one to handle a larger class of bilinear systems than the other observer based methods presented in the literature

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

a direct variational methods applied to burgers equation in this study a compact approximate method in limiting form for calculating the solution of burgers equation with appropriate boundary conditions is presented the results obtained by present method are found to be in good agreement with those due to earlier authors and offers appreciable advantages for burgers like nonlinear problems

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

new stability criteria for neural networks with time varying delays abstract this paper is concerned with the stability analysis problem of neural networks with time delays the delay intervals d t 0 and h 0 are divided into m subintervals with equal length some free matrices are introduced to build the relationship among the elements of the resultant matrix inequalities with the above operations the new stability criteria are built for the general class of neural networks the conditions are presented in the form of linear matrix inequalities lmis which can be solved by the numerically efficient matlab lmi toolbox several examples are provided to show that our methods are much less conservative than recently reported ones

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

observer based residual generation for fault diagnosis for non affine non linear polynomial systems this paper proposes an observer based residual generator obrg for diagnosing faults in a continuous non affine system with polynomial non linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output firstly given certain assumptions and the use of defined extended vectors a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate obrg conditions for error stability by a lyapunov method and detectability are given the calculation steps in the design of the obrg are shown to involve the solution of three linear equations with parameterizations and the calculation of a set of constant matrices for detectability of faults a result is then given establishing that the design holds for a much wider class of systems the residual design is applied to a real three tank system

passivity based control for hopfield neural networks using convex representation this paper considers the problem of passivity based controller design for hopfield neural networks by making use of a convex representation of nonlinearities a feedback control scheme based on passivity and lyapunov theory is presented a criterion for existence of the controller is given in terms of linear matrix inequality lmi which can be easily solved by a convex optimization problem an example and its numerical simulation are given to show the effectiveness of the proposed method

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

a difference scheme for burgers equation in an unbounded domain the numerical solution of the one dimensional burgers equation in an unbounded domain is considered two artificial boundaries are introduced to make the computational domain finite on both artificial boundaries two exact boundary conditions are proposed respectively to reduce the original problem to an initial boundary value problem in a finite computational domain a difference scheme is constructed by the method of reduction of order to solve the problem in the finite computational domain at each time level only a strictly diagonal dominated tridiagonal system of linear algebraic equations needs to be solved it is proved that the difference scheme is uniquely solvable and unconditional convergent with the convergence order 3 2 in time and order 2 in space in an energy norm a numerical example demonstrates the theoretical results

high order transverse schemes for the numerical solution of pdes many existing numerical schemes for the solution of initial boundary value problems for partial differential equations can be derived by the method of lines the pdes are converted into a system of ordinary differential equations either with initial conditions longitudinal scheme or with boundary conditions transverse scheme in particular this paper studies the performance of the transverse scheme in combination with boundary value methods moreover we do not restrict the semi discretization by the usual first or second order finite difference approximations to replace the derivative with respect to time but we use high order formulae

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

exponential stability analysis for uncertain neural networks with interval time varying delays in this paper the problem of exponential stability analysis for neural networks is investigated it is assumed that the considered neural networks have norm bounded parametric uncertainties and interval time varying delays by constructing a new lyapunov functional new delay dependent exponential stability criteria with an exponential convergence rate are established in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms two numerical examples are included to show the effectiveness of proposed criteria

improved delay dependent stability criterion for neural networks with time varying delay in this paper the problem of delay dependent asymptotic stability criterion for neural networks with time varying delay has been considered a new class of lyapunov functional which contains a triple integral term is constructed to derive some new delay dependent stability criteria the obtained criteria are less conservative because free weighting matrices method and a convex optimization approach are considered finally numerical examples are given to illustrate the effectiveness of the proposed method

an algorithm based on exponential modified cubic b spline differential quadrature method for nonlinear burgers equation in this paper the authors developed a new differential quadrature method exponential modified cubic b spline differential quadrature method expo mcb dqm by using exponential modified cubic b spline functions as test functions in the traditional differential quadrature method 32 the new method is tested on one and two dimensional nonlinear burgers equations to check the efficiency and accuracy of the proposed method five numerical problems have been considered the numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods stability analysis of the algorithm is also done by using matrix stability analysis method

fault detection observers for continuous non linear polynomial systems of general degree this paper proposes a robust fault detection observer rfdo for a continuous non linear system with polynomial non linearities up to any finite degree the observer error and residual are robust with respect to unknown inputs sufficient conditions are given in an efficient algebraic compact form for a rfdo observer and residual to exist useable results on detectablility conditions are proved numerical prodedures for the design of a rfdo and a sub optimal rfdo sorfdo are given the theory is illustrated with an application to a benchmark three tank system one linear and three non linear models are considered with corresponding rdfos including a sub optimal rfdo and the performances of the corresponding residuals are compared under two initial conditions for a scenario consisting of a leak fault and a disturbance

numerical methods for nonlinear second order hyperbolic partial differential equations ii rothe s techniques for 1 d problems abstract two families of rothe s methods that are based on the discretization of the time variable and keeping the spatial one continuous for the solution of second order hyperbolic equations with damping and nonlinear source terms are presented the first family is based on time integration and results in a volterra integro differential equation which upon approximating certain time integrals can be written as an ordinary differential equation in space upon discretizing the spatial derivatives by means of finite difference formula this family results in nonlinear algebraic equations which contain exponential terms that depend on the time step and its accuracy is shown to be lower than that of an explicit second order accurate discretization in both space and time of second order hyperbolic equations the second family of methods is based on the discretization of the time derivatives and time linearization and results in linear ordinary differential equations in space upon freezing the coefficients of these equations one can integrate analytically the resulting linear ordinary differential equations to obtain piecewise exponential solutions which are continuous in space and three point finite difference equations which depend exponentially on the time step spatial grid size and the diffusion relaxation damping and reaction times the finite difference equations are shown to result in non diagonally dominant matrices unless the time step is smaller than the characteristic relaxation diffusion damping and reaction times to avoid this problem two rothe s techniques that do not account for the jacobian of the reaction terms in the ordinary differential operator are developed and it is shown that the rothe s techniques belonging to the second family are as accurate as the linearly implicit methods presented in part i provided that the relaxation time is smaller than the critical time and the solution does not oscillate in space when the relaxation time is greater than the critical one rothe s methods have been found to be less accurate than the finite difference techniques of part i the rothe s techniques belonging to the second family are generalized to systems of nonlinear second order hyperbolic equations and mixed systems of parabolic and second order hyperbolic partial differential equations

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature