a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

integration schemes for von mises plasticity models based on exponential maps numerical investigations and theoretical considerations summary we consider three different exponential map algorithms for associative von mises plasticity with linear isotropic and kinematic hardening the first scheme is based on a different formulation of the time continuous plasticity model which automatically grants the yield consistency of the method in the numerical solution the second one is the quadratically accurate but non yield consistent method already proposed in auricchio and beirao da veiga int j numer meth engng 2003 56 1375 1396 the third method is an improved version of the second one in which the yield consistency condition is enforced a posteriori we also compare the performance of the three methods with the classical radial return map algorithm we develop extensive numerical tests which clearly show the main advantages and disadvantages of the three methods copyright 2005 john wiley sons ltd

reducing conservatism of stability criteria for linear systems with time varying delay using an improved triple integral inequality abstract this paper focuses on stability analysis of linear systems with time varying delay where two cases of the time varying delay are discussed that is the time varying delay is either differentiable or just uniformly continuous first an improved triple integral inequality is proposed to estimate triple integrals tightly then by introducing two novel lyapunov krasovskii functionals catering for two cases of time varying delay two sufficient conditions on stability respectively for the system under two cases of time varying delay are derived using the improved triple integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently finally three numerical examples show that the obtained results outperform some existing ones

a novel optimal exponential based integration algorithm for von mises plasticity with linear hardening theoretical analysis on yield consistency accuracy convergence and numerical investigations summary in this communication we propose a new exponential based integration algorithm for associative von mises plasticity with linear isotropic and kinematic hardening which follows the ones presented by the authors in previous papers in the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential based schemes and in particular we address the yield consistency exactness under proportional loading accuracy and stability of the methods in the second part of the contribution we show a detailed numerical comparison between the new exponential based method and two classical radial return map methods based on backward euler and midpoint integration rules respectively the developed tests include pointwise stress strain loading histories iso error maps and global boundary value problems the theoretical and numerical results reveal the optimal properties of the proposed scheme copyright 2006 john wiley sons ltd

on data dependence of exponential stability and stability radii for linear time varying differential algebraic systems abstract this paper is addressed to some questions concerning the exponential stability and its robustness measure for linear time varying differential algebraic systems of index 1 first the bohl exponent theory that is well known for ordinary differential equations is extended to differential algebraic equations then it is investigated that how the bohl exponent and the stability radii with respect to dynamic perturbations for a differential algebraic system depend on the system data the paper can be considered as a continued and complementary part to a recent paper on stability radii for time varying differential algebraic equations n h du v h linh stability radii for linear time varying differential algebraic equations with respect to dynamic perturbations j differential equations 230 2006 579 599

on stability of time varying linear differential algebraic equations we develop a stability theory for time varying linear differential algebraic equations daes well known stability concepts of ordinary differential equations are generalised to daes and characterised lyapunov s direct method is derived as well as the converse of the stability theorems stronger results are achieved for daes which are transferable into standard canonical form in this case the existence of the generalised transition matrix is exploited

a unified floquet theory for discrete continuous and hybrid periodic linear systems abstract in this paper we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts e g hybrid dynamical systems we develop a comprehensive floquet theory including lyapunov transformations and their various stability preserving properties a unified floquet theorem which establishes a canonical floquet decomposition on time scales in terms of the generalized exponential function and use these results to study homogeneous as well as nonhomogeneous periodic problems furthermore we explore the connection between floquet multipliers and floquet exponents via monodromy operators in this general setting and establish a spectral mapping theorem on time scales finally we show this unified floquet theory has the desirable property that stability characteristics of the original system can be determined via placement of an associated but time varying system s poles in the complex plane we include several examples to show the utility of this theory

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

novel inequality with application to improve the stability criterion for dynamical systems with two additive time varying delays abstract in this paper the stability of the system with two additive time varying delay components is studied and improved stability condition is obtained it firstly establishes two novel integral inequalities which are better than the same type inequalities found in the literature secondly a new constructed lyapunov functional is constructed based on the additive time varying delays property following two steps to handle the lyapunov functional the delay dependent stability condition is obtained which in terms of linear matrix inequalities finally two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results

on stabilisability of nonlinear systems on time scales in this article stabilisability of nonlinear finite dimensional control systems on arbitrary time scales is studied the classical results on stabilisation of nonlinear continuous time and discrete time systems are extended to systems on arbitrary time scales with bounded graininess function it is shown that uniform exponential stability of the linear approximation of a nonlinear system implies uniform exponential stability of the nonlinear system then this result is used to show a similar implication for uniform exponential stabilisability

construction of lyapunov krasovskii functionals for networks of iiss retarded systems in small gain formulation this paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation subsystems are assumed to be integral input to state stable iiss time delays are allowed to reside in both subsystems and interconnection channels and may be both discrete and distributed no assumption is made on the interconnection topology a small gain methodology is developed for constructing a lyapunov krasovskii functional to establish iiss of such a network

stability analysis of systems with time varying delays via the second order bessel legendre inequality this paper is concerned with the delay dependent stability of systems with time varying delays the novelty relies on the use of the second order bessel legendre integral inequality which is less conservative than the jensen and wirtinger based inequalities unlike similar contributions the features of this inequality are fully integrated into the construction of augmented lyapunov krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities the stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method

on the number of upper bohl exponents for diagonal discrete time varying linear system abstract the bohl exponents similarly as the lyapunov exponents are one of the most important numerical characteristics of dynamical systems used in control theory by contrast with properties of the lyapunov characteristics properties of the bohl exponents are much less investigated in this paper we present some new properties of the upper bohl exponents of the diagonal discrete time varying linear system

integration on time scales in this paper we study the process of riemann and lebesgue integration on time scales the relationship of the riemann and lebesgue integrals is considered and a criterion for riemann integrability is established

on the exponential stability of dynamic equations on time scales in this paper we deal with some theorems on the exponential stability of trivial solution of time varying non regressive dynamic equation on time scales with bounded graininess in particular well known perron s theorem is generalized on time scales under rather restrictive condition that is integral boundedness of coefficient operators we obtain a characterization of the uniformly exponential stability

bohl exponent for time varying linear differential algebraic equations we study stability of linear time varying differential algebraic equations daes the bohl exponent is introduced and finiteness of the bohl exponent is characterised the equivalence of exponential stability and a negative bohl exponent is shown and shift properties are derived we also show that the bohl exponent is invariant under the set of bohl transformations for the class of daes which possess a transition matrix introduced in this article the bohl exponent is exploited to characterise boundedness of solutions of a cauchy problem and robustness of exponential stability

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

an improved reciprocally convex inequality and an augmented lyapunov krasovskii functional for stability of linear systems with time varying delay this paper is concerned with stability of a linear system with a time varying delay first an optimal reciprocally convex inequality is proposed compared with the extended reciprocally convex inequality recently reported the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination but also introduces less slack matrix variables second a new lyapunov krasovskii functional is tailored for the use of auxiliary function based integral inequality third based on the optimal reciprocally convex inequality and the new lyapunov krasovskii functional a stability criterion is derived for the system under study finally two well studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time varying delay than some existing methods

on the integration schemes for drucker prager s elastoplastic models based on exponential maps rate plasticity equations for the case of drucker prager s model in small strain regime are considered by defining an augmented stress vector the formulations convert the original problem into a quasi linear differential equation system two new exponential mapping schemes for integrating model equations are proposed in addition two traditional schemes for solving the dynamical system in an explicit manner are discussed the two semi implicit schemes developed pose higher accuracy and better convergency error contours are provided for all four methods to display the accuracy of each scheme in order to compare the results these contours for the classical one step backward euler integration method are also displayed accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples copyright 2007 john wiley sons ltd

stability analysis of a class of switched linear systems on non uniform time domains abstract this paper deals with the stability analysis of a class of switched linear systems on non uniform time domains the considered class consists of a set of linear continuous time and linear discrete time subsystems first some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentially stable these results are extended when considering an unstable discrete time subsystem or an unstable continuous time subsystem some examples illustrate these results

on stability bohl exponent and bohl perron theorem for implicit dynamic equations in this paper we develop a stability theory for implicit dynamic equations which is a general form of differential algebraic equations and implicit difference equations we derive some results abo

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

on exponential dichotomy bohl perron type theorems and stability of difference equations abstract for a delay difference equation x n 1 k d n a n k x k f n in a banach space the following result is proved if for any f l p the solution is x l p then the solution of the homogeneous equation f 0 is exponentially stable this result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation