on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

robust h control for linear discrete time systems with norm bounded time varying uncertainty the problem of robust h analysis and synthesis for linear discrete time systems with norm bounded time varying uncertainty is studied in this paper it will be shown that this problem is equivalent to the problem of h analysis and synthesis of an auxiliary system the necessary and sufficient conditions for the equivalency are proved thus the original problem can be solved by existing h control methods

quaternion collaborative and sparse representation with application to color face recognition collaborative representation based classification crc and sparse rc src have recently achieved great success in face recognition fr previous crc and src are originally designed in the real setting for grayscale image based fr they separately represent the color channels of a query color image and ignore the structural correlation information among the color channels to remedy this limitation in this paper we propose two novel rc methods for color fr namely quaternion crc qcrc and quaternion src qsrc using quaternion ell 1 minimization by modeling each color image as a quaternionic signal they naturally preserve the color structures of both query and gallery color images while uniformly coding the query channel images in a holistic manner despite the empirical success of crc and src on fr a few theoretical results are developed to guarantee their effectiveness another purpose of this paper is to establish the theoretical guarantee for qcrc and qsrc under mild conditions comparisons with competing methods on benchmark real world databases consistently show the superiority of the proposed methods for both color fr and reconstruction

a new technique for velocity estimation of large moving objects a technique for motion estimation of large moving objects is presented this technique is based on analyzing the hartley transform spectrum of the image sequence directly instead of using it to compute other transforms in this technique the fast hartley transform fht is applied to the image sequence and followed by a peak detection procedure the location of the peak is related to the velocity of the moving object dividing the temporal frequency f sub p corresponding to the detected peak by the corresponding spatial frequency k sub p gives the velocity of the moving object the fourier spectrum for a spatial frequency of k sub p is then computed this is followed by a peak detection of the fourier spectrum to validate the previous results and find the direction of the velocity of the moving object this method is faster than other techniques based on the fourier transform

h sub infinity analysis and synthesis of discrete time systems with time varying uncertainty the problems of h sub infinity analysis and synthesis of discrete time systems with block diagonal real time varying uncertainty are considered it is shown that these problems can be converted into scaled h sub infinity analysis and synthesis problems the problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case the results on synthesis are established for general linear dynamic output feedback control

stability and stabilization of delay differential systems the delay systems considered here are represented by linear delay differential equations the system parameters and the delays are assumed to be imperfectly known the instantaneous state vector is perturbed by a bounded external disturbance vector the problem addressed is that of characterizing conditions that guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints it is shown that the positive invariance property can be used to solve this problem and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system the possible use of these results for the control of a multiple delay mimo differential model is then presented finally an example is given

a multi dimensional high order discontinuous galerkin method based on gas kinetic theory for viscous flow computations this paper presents a high order discontinuous galerkin dg method based on a multi dimensional gas kinetic evolution model for viscous flow computations generally the dg methods for equations with higher order derivatives must transform the equations into a first order system in order to avoid the so called non conforming problem in the traditional dg framework the inviscid and viscous fluxes are numerically treated differently differently from the traditional dg approaches the current method adopts a kinetic evolution model for both inviscid and viscous flux evaluations uniformly by using a multi dimensional gas kinetic formulation we can obtain a spatial and temporal dependent gas distribution function for the flux integration inside the cell and at the cell interface which is distinguishable from the gaussian quadrature point flux evaluation in the traditional dg method besides the initial higher order non equilibrium states inside each control volume a linear least square lls method is used for the reconstruction of smooth distributions of macroscopic flow variables around each cell interface in order to construct the corresponding equilibrium state instead of separating the space and time integrations and using the multistage runge kutta time stepping method for time accuracy the current method integrates the flux function in space and time analytically which subsequently saves the computational time many test cases in two and three dimensions which include high mach number compressible viscous and heat conducting flows and the low speed high reynolds number laminar flows are presented to demonstrate the performance of the current scheme

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

stability of x t ax t bx t tau a stability criterion for linear time delay systems described by a differential difference equation of the form dx t ax t bx t tau is proposed the result obtained includes information on the size of the delay and therefore can be a delay dependent stability condition its relation to existing delay independent stability criteria is also discussed

a differential equation approach to the computation of the fourier transform of the images of translating objects the frequency domain analysis of constant velocity motion has proven useful in a number of different contexts ranging from television signal processing to computer vision this work considers the frequency domain analysis of a generalization of such simple dynamics which includes the effect of acceleration and its time derivatives of any order in the frequency domain the contribution due to the object s shape and the contribution due to translation terms are clearly separated motion information in the frequency domain is given by functions characterized by a family of differential equations such differential equations are introduced in the work and their solutions are exemplified in order to compute the frequency domain motion contributions for simplicity the results are presented for the case of translations but they apply equally well to rotations

adaptive moving grid methods for two phase flow in porous media a b s t r a c t in this paper we present an application of the moving mesh method for approximating numerical solutions of the two phase flow model in porous media the numerical schemes combine a mixed finite element method and a finite volume method which can handle the nonlinearities of the governing equations in an efficient way the adaptive moving grid method is then used to distribute more grid points near the sharp interfaces which enables us to obtain accurate numerical solutions with fewer computational resources the numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two phase flows in porous media

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

an element wise locally conservative galerkin lcg method for solving diffusion and convection diffusion problems an element wise locally conservative galerkin lcg method is employed to solve the conservation equations of diffusion and convection diffusion this approach allows the system of simultaneous equations to be solved over each element thus the traditional assembly of elemental contributions into a global matrix system is avoided this simplifies the calculation procedure over the standard global continuous galerkin method in addition to explicitly establishing element wise flux conservation in the lcg method elements are treated as sub domains with weakly imposed neumann boundary conditions the lcg method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging it is also shown in this paper that the proposed lcg method is identical to the standard global galerkin gg method at both steady and unsteady states for an inside node thus the method has all the advantages of the standard gg method while explicitly conserving fluxes over each element several problems of diffusion and convection diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the lcg method both linear and quadratic elements are used in the calculations for convection dominated problems petrov galerkin weighting and high order characteristic based temporal schemes have been implemented into the lcg formulation

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

spatiotemporal wavelets a group theoretic construction for motion estimation and tracking this paper presents a new group theoretic perspective for signal and image analysis it addresses the problem of motion analysis and trajectory determination the construction exploits the properties of motion parameters to be structured in lie algebras and lie groups the motion models are provided by the group structure which carries an entire theoretical build up this theoretical construction is based on a natural association of lie group representations minimum mean squared error estimations and variational principles of optimality these concepts naturally provide a corresponding association of tools based on continuous wavelet transforms kalman filters and lagrangians these tools result in highly parallelizable algorithms based on ffts gradients and dynamic programming the core of the construction is made of spatiotemporal continuous wavelets that are tuned to the motion parameters to perform motion estimation the motion parameters consist of scale orientation location velocity acceler

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

h control of discrete time linear systems with time varying delays in state this paper deals with the h control problems for discrete time linear systems with time varying delays in state in this paper the h control law is assumed to be a memoryless state feedback and the size of time varying delays considered is upper bounded the solution of the h control problem for discrete time linear systems with time varying delays in state can be obtained by solving an h control problem for auxiliary discrete time linear systems with no time delays

on convergence of finite volume schemes for one dimensional two phase flow in porous media this paper deals with development and analysis of finite volume schemes for a one dimensional nonlinear degenerate convection diffusion equation having application in petroleum reservoir and groundwater aquifer simulation the main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term we analyze and compare three families of numerical schemes corresponding to explicit semi implicit and implicit discretization of the diffusion term and a godunov scheme for the advection term l stability under appropriate cfl conditions and bv estimates are obtained it is shown that the schemes satisfy a discrete maximum principle then we prove convergence of the approximate solution to the weak solution of the problem results of numerical experiments using the present approach are reported

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

hypercomplex correlation techniques for vector images correlation techniques have been applied to almost every area of signal processing over the past century yet their use has in general been limited to scalar signals while there have been implementations in multichannel applications these can be characterized as a combination of single channel processes true vector correlation techniques with global and interchannel measures have only recently been demonstrated and are still in their infancy by comparison this paper describes our work on vector correlation based on the use of hypercomplex fourier transforms and presents for the first time a unified theory behind the information contained in the peak of a vector correlation response by using example applications for color images we also demonstrate some of the practical implications together with our latest results

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

a weighted difference scheme and monotone iterative methods for quasilinear boundary value problems abstract we consider the boundary value problem y xx f x y y x g x y 0 0 x y 0 b 0 y 1 b 1 we present a weighted two sided difference scheme to approximate the differential equation monotone iterative methods are proposed to solve the resulting nonlinear system the scheme applies equally well to multidimensional analogues numerical results are included

output feedback stabilization for a discrete time system with a time varying delay this study employs the free weighting matrix approach to investigate the output feedback control of a linear discrete time system with an interval time varying delay first the delay dependent stability is analyzed using a new method of estimating the upper bound on the difference of a lyapunov function without ignoring any terms and based on the results a design criterion for a static output feedback sof controller is derived since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility sof control problem furthermore the problem of designing a dynamic output feedback controller is formulated as one of designing an sof controller numerical examples demonstrate the effectiveness of the method and its advantage over existing methods

on stability independent of delay for linear systems a new criterion for asymptotic stability of solutions of certain linear differential difference equations independent of the delay duration is given in terms of solutions of a complex lyapunov matrix equation

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

two dimensional matched filtering for motion estimation in this work we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence the least squares optimum approach involves the computation of the three dimensional 3 d fourier transform of the sequence followed by the detection of one or more planes in this domain with high energy concentration we present a more efficient algorithm based on the properties of the radon transform and the two dimensional 2 d fast fourier transform which can sacrifice little performance for significant computational savings we accomplish the motion detection and estimation by designing appropriate matched filters the performance is demonstrated on two image sequences

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

a finite element method for the 1 d water flooding problem with gravity abstract the numerical simulation of the one dimensional displacement of oil by water in a vertical porous slab is studied the water saturation is governed by a quasilinear diffusion convection equation the diffusion term vanishes for the extreme values of the saturation the transport term may be nonmonotone for small or zero water injection rates in presence of gravity various boundary conditions are used a generalized dirichlet condition for the pure transport case and a condition taking into account the so called well effect on the production boundary for the case with capillary diffusion the above problem is solved using discontinuous finite elements together with mixed finite elements following the ideas of lesaint raviart and thomas godunov s generalization of upstream weighting is also incorporated a computer code of this algorithm works satisfactorily under a wide range of experimental conditions going from the pure diffusion case 0 to the pure transport case 0 results of various runs on idealized data as well as on laboratory data are shown

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

robust observer based h controller design for linear uncertain time delay systems in this note we present a robust observer based h control design method for linear time delay systems with norm bounded time varying uncertainties using the riccati equation based approach we design observer based feedback control laws which guarantee the quadratic stability of the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

quaternion bessel fourier moments and their invariant descriptors for object reconstruction and recognition in this paper the quaternion bessel fourier moments are introduced the significance of phase information in quaternion bessel fourier moments is investigated and an accurate estimation method for rotation angle is described furthermore a new set of invariant descriptors based on the magnitude and the phase information of quaternion bessel fourier moments is derived experimental results show that quaternion bessel fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion zernike moments quaternion pseudo zernike moments and quaternion orthogonal fourier mellin moments in addition the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments the proposed invariant descriptors show also better robustness to geometric and photometric transformations quaternion bessel fourier moments for color image reconstruction and recognition an accurate estimation method for rotation angle throughout quaternion moments the invariant descriptor using the moment magnitudes and phase coefficients

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

delay dependent robust h control of uncertain linear systems with time varying delays abstract this paper proposes an optimization based approach to the robust h control problem of uncertain continuous or discrete time linear time invariant systems with different time varying delays in the state vector and control input of the dynamic equation and controlled output sufficient delay dependent conditions are derived for the control stabilization problem where both the size of the time varying delay and the size of its time derivative in the continuous time case play a crucial role for the closed loop stability with a guaranteed h performance index the solutions that are proposed for the h control problem are similar or less conservative when compared to other recent approaches