improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

the solution methods for the largest eigenvalue singular value of nonnegative tensors and convergence analysis abstract in this paper we study two solution methods for finding the largest eigenvalue singular value of general square rectangular nonnegative tensors for a positive tensor one can find the largest eigenvalue singular value based on the properties of the positive tensor and the power type method while for a general nonnegative tensor we use a series of decreasing positive perturbations of the original tensor and repeatedly recall power type method for finding the largest eigenvalue singular value of a positive tensor with an inexact strategy we prove the convergence of the method for the general nonnegative tensor under a certain assumption the computing complexity of the method is established motivated by the interior point method for the convex optimization we put forward a one step inner iteration power type method whose convergence is also established under certain assumption additionally by using embedding technique we show the relationship between the singular values of the rectangular tensor and the eigenvalues of related square tensor which suggests another way for finding the largest singular value of nonnegative rectangular tensor besides direct power type method for this problem finally numerical examples of our algorithms are reported which demonstrate the convergence behaviors of our methods and show that the algorithms presented are promising

singular values of a real rectangular tensor real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics in this paper we systematically study properties of singular values of a real rectangular tensor and give an algorithm to find the largest singular value of a nonnegative rectangular tensor numerical results show that the algorithm is efficient

singular value inclusion sets of rectangular tensors abstract in this paper two singular value inclusion sets for rectangular tensors via a digraph and a lifting square tensor are given respectively furthermore it is shown that these two singular value inclusion sets are both tighter than the known result given by zhao and li in theorem 2 1 of 25 and singular value inclusion sets via a digraph in special case are tighter than the inclusion sets via a lifting square tensor numerical examples are still given to show the relation among the inclusion sets via a digraph the inclusion sets via a lifting square tensor and the known result given by zhao and li 25 finally by using the lifting square tensors the result of tensors provided by bu et al 24 is extended to rectangular tensors

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

robust stability criteria for systems with interval time varying delay and nonlinear perturbations this paper considers the robust stability for a class of linear systems with interval time varying delay and nonlinear perturbations a lyapunov krasovskii functional which takes the range information of the time varying delay into account is proposed to analyze the stability a new approach is introduced for estimating the upper bound on the time derivative of the lyapunov krasovskii functional on the basis of the estimation and by utilizing free weighting matrices new delay range dependent stability criteria are established in terms of linear matrix inequalities lmis numerical examples are given to show the effectiveness of the proposed approach

lmi approach to exponential stability of linear systems with interval time varying delays abstract this paper addresses exponential stability problem for a class of linear systems with time varying delay the time delay is assumed to be a continuous function belonging to a given interval but not necessary to be differentiable by constructing a set of augmented lyapunov krasovskii functional combined with the newton leibniz formula technique new delay dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities lmis an application to exponential stability of uncertain linear systems with interval time varying delay is given numerical examples are given to show the effectiveness of the obtained results

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

unstructured viscous grid generation by the advancing layers method a new method of generating unstructured triangular tetrahedral grids with high aspect ratio cells is proposed the method is based on new grid marching strategy referred to as advancing layers for construction of highly stretched cells in the boundary layer and the conventional advancing front technique for generation of regular equilateral cells in the inviscid flow region unlike the existing semi structured viscous grid generation techniques the new procedure relies on a totally unstructured advancing front grid strategy resulting in a substantially enhanced grid flexibility and efficiency the method is conceptually simple but powerful capable of producing high quality viscous grids for complex configurations with ease a number of two dimensional triangular grids are presented to demonstrate the methodology the basic elements of the method however have been primarily designed with three dimensional problems in mind making it extendible for tetrahedral viscous grid generation

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

a tensor product matrix approximation problem in quantum physics we consider a matrix approximation problem arising in the study of entanglement in quantum physics this notion represents a certain type of correlations between subsystems in a composite quantum system the states of a system are described by a density matrix which is a positive semidefinite matrix with trace one the goal is to approximate such a given density matrix by a so called separable density matrix and the distance between these matrices gives information about the degree of entanglement in the system separability here is expressed in terms of tensor products we discuss this approximation problem for a composite system with two subsystems and show that it can be written as a convex optimization problem with special structure we investigate related convex sets and suggest an algorithm for this approximation problem which exploits the tensor product structure in certain subproblems finally some computational results and experiences are presented

stability analysis of linear systems with two delays of overlapping ranges in this paper a delay dependent stability criterion is derived for linear time delay systems with two constant delays having overlapping ranges this overlapping feature of the delays is exploited in delay dependent analysis of the system using lyapunov krasovskii approach the developed treatment of the delays reduces conservatism in analysis compared to the approaches treating the delays individually numerical examples are used to demonstrate the less conservativeness of the derived criterion

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

delay dependent stability analysis for a class of dynamical systems with leakage delay and nonlinear perturbations this paper studies the stability problem for a class of dynamical systems with leakage delay and nonlinear perturbations based on linear matrix inequality lmi approach some sufficient conditions which are dependent on the leakage delay are derived to ensure the global asymptotic stability by using lyapunov krasovskii functional method and free weighting matrix technique two examples and their simulations are given to show the effectiveness and advantage of the present results

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

influence of impingement edge geometry on cavity flow oscillations and back portion of the airfoil is shown in figs 2b and 2c respectively the smooth transition of the grid from one type to another and the decency of the grid at sharp corners and between close surfaces are clearly shown which indicate excellent compatibility and communication between the two grid strategies as controlled by a common background grid the grid was generated using a silicon graphics iris 4d 210 vox workstation the code s performance is about 360 triangles s on that workstation and 2350 triangles s on a cray y mp the total turnaround time required for generating a grid around a complex geometry including the setup time is about 1 h to examine the fidelity of the grids generated with the present method a turbulent viscous flow computation was performed on the grid shown in fig 2 the flow solution was obtained with an available node based upwind flow solver8 using the baldwinearth turbulence model at a mach number of 0 2 an angle of attack of 16 2 deg and a reynolds number of 9 x 106 comparisons for surface pressure distributions and velocity profiles are shown in figs 3a and 3b respectively excellent agreement with experimental data confirms the viability of the generated grid concluding remarks a new method of unstructured viscous grid generation has been introduced the approach is conceptually simple but powerful and capable of producing high quality viscous unstructured grids for complex configurations with ease being based on a totally unstructured grid strategy the method is fully automatic and flexible and thus alleviates the difficulties stemming from the structural limitations of the existing structured or semi unstruct ured techniques because of an efficient grid marching strategy and a simple front detection algorithm the method is highly efficient and operational on small workstations the method is also self sufficient for insertion of grid points in the boundary layer and beyond the method has been applied to two dimensional problems with satisfactory results the basic elements of the technique however have been primarily designed for its subsequent extension for generating three dimensional highly stretched tetrahedral grids which is currently in progress the full benefit of the method will be realized for generation of three dimensi onal viscous grids where the complexity of the problem becomes excessive

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

novel delay dependent stability criterion for time varying delay systems with parameter uncertainties and nonlinear perturbations this study proposes a novel approach to obtain less conservative conditions for the robust stability analysis for time varying delay systems with parameter uncertainties and nonlinear perturbations specifically first we divide the time varying delay into non uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms more exactly second novel delay derivation dependent stability criteria are derived by introducing a parameter c in the lyapunov krasovskii functional third we define some new variables to deal with uncertain parameters finally two numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results

inhomogeneous polynomial optimization over a convex set an approximation approach in this paper we consider computational methods for optimizing a multivariate inhomogeneous polynomial function over a general convex set the focus is on the design and analysis of polynomial time approximation algorithms the methods are able to deal with optimization models with polynomial objective functions in any fixed degrees in particular we first study the problem of maximizing an inhomogeneous polynomial over the euclidean ball a polynomial time approximation algorithm is proposed for this problem with an assured relative worst case performance ratio which is dependent only on the dimensions of the model the method and approximation ratio are then generalized to optimize an inhomogeneous polynomial over the intersection of a finite number of co centered ellipsoids furthermore the constraint set is extended to a general convex compact set specifically we propose a polynomial time approximation algorithm with a relative worst case performance ratio for polynomial optimization over some convex compact sets e g a polytope finally numerical results are reported revealing good practical performance of the proposed algorithms for solving some randomly generated instances

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

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

a novel result on stability analysis for uncertain neutral stochastic time varying delay systems generalized finsler lemma is applied to deduce delay dependent stability conditions the case is considered that the discrete delay is different from the neutral delay model transformation cross terms estimation and free weighting matrices are avoided the conditions show less conservatism and involves fewer computational variables numerical examples show that the proposed approach improves some existing ones this paper is concerned with the mean square exponential stability analysis for uncertain neutral linear stochastic time varying delay systems by lyapunov krasovskii theory and linear matrix inequality method under the generalized finsler lemma gfl framework delay dependent mean square exponential stability criteria are established without involving model transformation cross terms bounding technique or additional free weighting matrix moreover gfl is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing results

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

maximum block improvement and polynomial optimization in this paper we propose an efficient method for solving the spherically constrained homogeneous polynomial optimization problem the new approach has the following three main ingredients first we establish a block coordinate descent type search method for nonlinear optimization with the novelty being that we accept only a block update that achieves the maximum improvement hence the name of our new search method maximum block improvement mbi convergence of the sequence produced by the mbi method to a stationary point is proved second we establish that maximizing a homogeneous polynomial over a sphere is equivalent to its tensor relaxation problem thus we can maximize a homogeneous polynomial function over a sphere by its tensor relaxation via the mbi approach third we propose a scheme to reach a kkt point of the polynomial optimization provided that a stationary solution for the relaxed tensor problem is available numerical experiments have shown that our new method works very efficiently for a majority of the test instances that we have experimented with the method finds the global optimal solution at a low computational cost

stability analysis and controller synthesis for discrete time delayed fuzzy systems via small gain theorem this paper investigates the problems of stability analysis and controller synthesis of discrete time takagi sugeno t s fuzzy systems with time varying delay via an input output approach the original system is reformulated as a feedback subsystem and a forward subsystem with two constant time delays and a delay uncertainty satisfying the scaled small gain theorem the lifting method is employed to convert the forward subsystem to a delay free system where the main result concerning the stability analysis of the system is obtained based on the scaled small gain theorem the merit of the new stability condition lies in its reduced conservatism which is made possible by a more precise estimation of the time varying delay additionally a state feedback controller is designed through the lyapunov krasovskii functional approach combined with the utilization of the scaled small gain theorem two illustrative examples are given to demonstrate the less conservatism of the stability condition and the effectiveness of the controller design method

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

m eigenvalue inclusion intervals for a fourth order partially symmetric tensor abstract m eigenvalues of a fourth order partially symmetric tensor play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics but it is not easy to get the m eigenvalues exactly especially for high dimensional fourth order partially symmetric tensors in this paper we give two m eigenvalue inclusion intervals for a fourth order partially symmetric tensor which provide two upper bounds for the m spectral radius as an application taking these upper bounds as the parameter in wqz algorithm presented by wang et al 2009 respectively can make the generated sequence by this algorithm more rapidly converge to a good approximation of the largest m eigenvalue of a fourth order partially symmetric tensor

brief paper exponential stability of singular systems with multiple time varying delays this paper deals with the class of continuous time singular linear systems with multiple time varying delays in a range the global exponential stability problem of this class of systems is addressed delay range dependent sufficient conditions such that the system is regular impulse free and a stable are developed in the linear matrix inequality lmi setting moreover an estimate of the convergence rate of such stable systems is presented a numerical example is employed to show the usefulness of the proposed results

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

convergence of an algorithm for the largest singular value of a nonnegative rectangular tensor abstract in this paper we present an iterative algorithm for computing the largest singular value of a nonnegative rectangular tensor we establish the convergence of this algorithm for any irreducible nonnegative rectangular tensor

biquadratic optimization over unit spheres and semidefinite programming relaxations this paper studies the so called biquadratic optimization over unit spheres min x in mathbb r n y in mathbb r m sum 1 leq i k leq n 1 leq j l leq m b ijkl x i y j x k y l subject to x 1 y 1 we show that this problem is np hard and there is no polynomial time algorithm returning a positive relative approximation bound then we present various approximation methods based on semidefinite programming sdp relaxations our theoretical results are as follows for general biquadratic forms we develop a frac 1 2 max m n 2 approximation algorithm under a slightly weaker approximation notion for biquadratic forms that are square free we give a relative approximation bound frac 1 nm when min n m is a constant we present two polynomial time approximation schemes ptass which are based on sum of squares sos relaxation hierarchy and grid sampling of the standard simplex for practical computational purposes we propose the first order sos relaxation a convex quadratic sdp relaxation and a simple minimum eigenvalue method and show their error bounds some illustrative numerical examples are also included

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

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

distinguishing separable and entangled states we show how to design families of operational criteria that distinguish entangled from separable quantum states the simplest of these tests corresponds to the well known peres horodecki positive partial transpose ppt criterion and the more complicated tests are strictly stronger the new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs we successfully applied the results to many low dimensional states from the literature where the ppt test fails as a by product of the criteria we provide an explicit construction of the corresponding entanglement witnesses

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

new results on a delay derivative dependent fuzzy h infty filter design for t s fuzzy systems this paper focuses on the fuzzy h filter design problem for takagi sugeno t s fuzzy systems with interval time varying delays two cases of the time varying delays are considered 1 the delays are differentiable and have both the lower and upper bounds of the delay derivatives and 2 the delays are bounded but not necessary to be differentiable since we employ a new fuzzy lyapunov krasovskii functional lkf and estimate a tighter upper bound of its derivative the proposed delay derivative dependent bound real lemma brl condition has advantages over some previous results in that it enlarges the application scope but has less conservatism which is established theoretically the brl condition that depends on both the upper and lower bounds of the delay derivatives is derived then based on the aforesaid brl a new fuzzy h filter scheme is proposed and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities lmis finally some numerical examples and an application to the truck trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

technical communique new stability criteria for linear systems with interval time varying delay this paper investigates robust stability of uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and is a fast time varying function the uncertainty under consideration includes polytopic type uncertainty and linear fractional norm bounded uncertainty a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the interval time varying delay is proposed to drive some new delay dependent stability criteria in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no redundant matrix variable is introduced finally three numerical examples are given to show the effectiveness of the proposed stability criteria

delay partitioning approach for systems with interval time varying delay and nonlinear perturbations this paper considers the problem of robust stability for a class of linear systems with interval time varying delay and nonlinear perturbations less conservative stability criteria was put forward by using delay partitioning approach by decomposing the delay interval into multiple equidistant subintervals new lyapunov krasovskii l k functional contains some triple integral terms and augment terms which are introduced on these intervals thus resulting in being much less conservative than most existing results in the literature in addition in deriving the stability conditions in linear matrix inequality lmi framework neither model transformations nor superfluous free weighting matrix are employed for dealing the cross terms that emerge from the time derivative of the l k functional instead they are dealt using tighter integral inequalities which only contain a minimal number of slack matrix variables numerical examples are given to demonstrate the effectiveness of the proposed approach

delay dependent state feedback stabilization for a networked control model with two additive input delays this paper is centered on delay dependent state feedback stabilization for a networked control model with two additive input delays firstly delay dependent stability is investigated by splitting the whole delay interval into subintervals according to the delays a lyapunov functional is constructed to reduce conservatism we handle the lyapunov functional in two ways more specifically we take the lyapunov functional as a whole to examine its positive definite rather than restrict each term of it to positive definite as usual in addition when estimating the derivative of the lyapunov functional we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals the resulting stability results turn out dependent on the two delays separately and less conservative than some existing ones then based on the stability results state feedback stabilization is studied delay dependent conditions are formulated for the controller such that the closed loop system is asymptotically stable finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method

on copositiveness identification of partially symmetric rectangular tensors abstract this paper studies the copositiveness of a partially symmetric rectangular tensor some new criteria for identifying copositive rectangular tensors are established via the representation of the multivariate form in barycentric coordinates based on this we propose a numerical method for identifying the copositiveness of a partially symmetric rectangular tensor preliminary numerical results are reported to show the efficiency of the proposed method

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

structured background grids for generation of unstructured grids by advancing front method a new method of background grid construction is introduced for generation of unstructured grids using the advancing front technique unlike the conventional triangular tetrahedral background grids that are difficult to construct and usually inadequate in performance the new method exploits the simplicity of uniform cartesian meshes and the superiority of the elliptic grid point distribution for unstructured grid generation the approach is analogous to solving a steady state heat conduction problem with discrete heat sources the spacing parameters of grid points are distributed over the nodes of a cartesian background grid by solving a poisson equation to increase the control over the grid point distribution a directional clustering approach is developed the new method is convenient to use and provides better grid quality and flexibility some sample two dimensional results are presented to demonstrate the power of the method

robust stabilization for non linear discrete time systems this paper deals with the problem of robust stabilization for linear discrete time systems under non linear perturbations without limitation to single input systems and restriction on the structures of both the positive definite matrix and the corresponding variable a new sufficient condition is presented which guarantees the stability of the closed loop system and at the same time maximizes the bound on the non linearity in addition our main result is extended to discrete time delay systems all the conditions are given within the framework of linear matrix inequalities the effectiveness of the methods is illustrated with three examples

passive control for singular time delay system with actuator saturation this paper considers the problem of passivity controller design for singular time delay system with actuator saturation and nonlinear disturbance firstly by tuning the wirtinger based integral inequality a sufficient condition is derived to guarantee that the nonlinear singular time delay system is regular impulse free asymptotically stable with the dissipation performance then based on the derived condition and applying linear matrix inequalities lmis techniques the passive state feedback controller is synthesized moreover the maximal estimate of the domain of attraction is proposed by an optimization problem finally some numerical examples are given to illustrate the effectiveness of the obtained theoretic results

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

technical communique delay dependent robust stability for uncertain linear systems with interval time varying delay this paper is concerned with the delay dependent robust stability problem for uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and no restriction on the derivative of the time varying delay is needed which allows the delay to be a fast time varying function the uncertainty under consideration is norm bounded and possibly time varying uncertainty based on the lyapunov krasovskii functional approach a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria numerical examples are given to demonstrate effectiveness of the proposed method

approximation algorithms for homogeneous polynomial optimization with quadratic constraints in this paper we consider approximation algorithms for optimizing a generic multi variate homogeneous polynomial function subject to homogeneous quadratic constraints such optimization models have wide applications e g in signal processing magnetic resonance imaging mri data training approximation theory and portfolio selection since polynomial functions are non convex the problems under consideration are all np hard in general in this paper we shall focus on polynomial time approximation algorithms in particular we first study optimization of a multi linear tensor function over the cartesian product of spheres we shall propose approximation algorithms for such problem and derive worst case performance ratios which are shown to be dependent only on the dimensions of the model the methods are then extended to optimize a generic multi variate homogeneous polynomial function with spherical constraint likewise approximation algorithms are proposed with provable approximation performance ratios furthermore the constraint set is relaxed to be an intersection of co centered ellipsoids namely we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin and propose polynomial time approximation algorithms with provable worst case performance ratios numerical results are reported illustrating the effectiveness of the approximation algorithms studied