complete quadratic lyapunov functionals for distributed delay systems this paper is concerned with the stability analysis of distributed delay systems using complete lyapunov functionals numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling the interest of such approximations is the design of tractable sufficient stability conditions in the present article we provide an alternative method based on polynomial approximation which takes advantages of the legendre polynomials and their properties the resulting stability conditions are scalable with respect to the maximum degree of the polynomials and are expressed in terms of tractable linear matrix inequalities several examples of delayed systems are tested to show the effectiveness of the method

comparison of grid euler deconvolution with and without 2d constraints using a realistic 3d magnetic basement model we describe the application of a 2d constrained grid euler deconvolution method which is able to determine for each solution window whether the source structure is two dimensional three dimensional or poorly defined and to estimate the source location and depth in each solution window eigenvalues and eigenvectors are derived from the euler equations and compared to threshold levels a single eigenvalue below the given threshold and lying in the x y plane is shown to indicate a 2d source while the absence of such an eigenvalue indicates a 3d source geometry two small eigenvalues indicate the field in the window has no distinct source applying these criteria to each solution window allows us to generate a map of source geometry distribution we evaluate the effectiveness of 2d constrained grid euler deconvolution using synthetic magnetic data generated from a 3d basement model based on real topography from an area with surface exposed faulting this modeling strategy provides a complex nonidealized data set that compares euler depth estimates directly to the known basement surface depth our results indicate that noninteger structural indices can be the most appropriate choice for some data sets and the 2dconstrained grid euler method images magnetic basement structure more clearly and unambiguously than the conventional grid euler method

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

magnetic interpretation in three dimensions using euler deconvolution magnetic survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using euler s homogeneity relation the method employs gradients either measured or calculated data need not be pole reduced so that remanence is not an interfering factor geologic constraints are imposed by use of a structural index model studies show that the method can locate or outline confined sources vertical pipes dikes and contacts with remarkable accuracy a field example using data from an intensively studied area of onshore britain shows that the method works well on real data from structurally complex areas and provides a series of depth labeled euler trends which mark magnetic edges notably faults with good precision

three dimensional interpretation of magnetic and gravity anomalies using the finite difference similarity transform we present an automatic procedure for interpretation of magnetic or gravity gridded anomalies based on the finite difference similaritytransformfdst itiscalledmagsoundfdstmagneticandgravitysoundingbasedonthefinite differencesimilarity transform and uses a focusing principle in contrast to deriving multiple clusters of many solutions as in the widely used euler deconvolution method the source parameters are characterized by isolated solutions and the interpreter obtains parallel images showing the horizontal position depth and structural index n value the underlying principle is that the fdst of a potential field anomaly becomes zero or linear at all observation pointswhenthecentralpointofsimilaritycpsofthetransform coincides with a sourcefield s singular point and a correctn valueisused theprocedureinvolvescalculatinga3dfunctionthat evaluatesthelinearityofthefdstforaseriesofn values using a moving window and sounding the subsurface along a vertical line under each window center we then combine the 3d results fordifferentnvaluesintoasinglemapwhoseminimadetermine the horizontal position of the sources the n value and the cps depth associated with each minimum determine the n value and depth of the corresponding source only one estimate characterizes a simple source which is a major advantage over other window based procedures magsoundfdst uses only the measuredanomalousfieldanditsupwardcontinuation thusavoiding thedirectuseoffieldderivatives itisindependentofthemagnetization vector direction in the magnetic data case the procedureaccountsforalinearbackgroundoflocalgravityormagnetic anomalies and has been applied effectively to several cases of synthetic and real data magsoundfdst shares common featureswiththemagneticandgravitysoundingbasedonthedifferential similarity transform magsounddst but is more stable in estimating depth and structural index in the presence of randomnoise

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

comparison of some bounding inequalities applied in stability analysis of time delay systems abstract this paper gives comparisons of several bounding inequalities proposed recently for the estimation of integrals and sums of quadratic functions which plays an important role in stability analysis of time delay systems via the lyapunov krasovskii approach the equivalences of several known variants of the free matrix based inequalities and their generalized and simplified forms are shown secondly the relationship between the simplified free matrix based inequality and the combination of the bessel based inequality with different bounding inequalities affine in the length of the intervals are investigated finally we shall demonstrate the theoretical results with the application of the various estimations for the stability analysis of a linear system with time varying delay using the same lyapunov krasovskii functional

stability analysis of linear coupled differential difference systems with general distributed delays we present a new approach for the stability analysis of linear coupled differential difference systems with a general distributed delay the distributed delay term in this note can contain any mathbb l 2 function which is approximated via a class of elementary functions including polynomial trigonometric exponential functions etc through the application of a new proposed integral inequality a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a lyapunov krasovskii functional the methods proposed in this note can handle problems that cannot be dealt using existing approaches two numerical examples are presented to show the effectiveness of our proposed stability condition

deterministic generalized automata a generalized automaton ga is a finite automaton where the single transitions are defined on words rather than on single letters generalized automata were considered by k hashiguchi who proved that the problem of calculating the size of a minimal ga is decidable

deciding determinism of caterpillar expressions caterpillar expressions have been introduced by bruggemann klein and wood for applications in markup languages caterpillar expressions provide a convenient formalism for specifying the operation of tree walking automata on unranked trees here we give a formal definition of determinism of caterpillar expressions that is based on the language of instruction sequences defined by the expression we show that determinism of caterpillar expressions can be decided in polynomial time

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

multiple integral inequalities and stability analysis of time delay systems abstract this paper is devoted to stability analysis of continuous time delay systems based on a set of lyapunov krasovskii functionals new multiple integral inequalities are derived that involve the famous jensen s and wirtinger s inequalities as well as the recently presented bessel legendre inequalities of seuret and gouaisbaut 2015 and the wirtinger based multiple integral inequalities of park et al 2015 and lee et al 2015 the present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of lmis establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods numerical examples illustrate the efficiency of the method

tractable sufficient stability conditions for a system coupling linear transport and differential equations abstract this paper deals with the stability analysis of a system of finite dimension coupled to a vectorial transport equation we develop here a new method to study the stability of such a system coupling ordinary and partial differential equations using linear matrix inequalities led by the choice of an appropriate lyapunov functional to this end we exploit legendre polynomials and their properties and use a bessel inequality to measure the contribution of our approximation the exponential stability of a wide class of delay systems is a direct consequence of this study but above all we are detailing here a new approach in the consideration of systems coupling infinite and finite dimensional dynamics the coupling with a vectorial transport equation is a first step that already prove the interest of the method bringing hierarchized conditions for stability we will give exponential stability results and their proofs our approach will finally be tested on several academic examples

expansions in series of orthogonal hypergeometric polynomials abstract let us consider an arbitrary hypergeometric polynomial qj x and a set of orthogonal hypergeometric polynomials p n x in the domain of orthogonality here the expansion coefficients of xm and xmqj x m n0 in series of the set p n x are found in terms of the polynomials x and x characterizing the second order differential equations satisfied by the involved hypergeometric polynomials the resulting general expressions which are given in an explicit and compact form are used to produce known for checking and unknown expansions for various concrete classical orthogonal polynomials

on the power of tree walking automata tree walking automata twas recently received new attention in the fields of formal languages and databases to achieve a better understanding of their expressiveness we characterize them in terms of transitive closure logic formulas in normal form it is conjectured by engelfriet and hoogeboom that twas cannot define all regular tree languages or equivalently all of monadic second order logic we prove this conjecture for a restricted but powerful class of twas in particular we show that 1 bounded twas that is twas that are only allowed to traverse every edge of the input tree at most once in every direction cannot define all regular languages we then extend this result to a class of twas that can simulate first order logic fo and is capable of expressing properties not definable in fo extended with regular path expressions the latter logic being a valid abstraction of current query languages for xml and semistructured data

tree walking automata do not recognize all regular languages tree walking automata are a natural sequential model for recognizing tree languages it is well known that every tree language recognized by a tree walking automaton is regular we show that the converse does not hold

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

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

stability analysis of linear systems with interval time varying delays utilizing multiple integral inequalities this paper is devoted to stability analysis of continuous time delay systems with interval time varying delays having known bounds on the delay derivatives a parameterized family of lyapunov krasovskii functionals involving multiple integral terms is introduced and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time varying delays the efficiency of the proposed method is illustrated by numerical examples

multiridge analysis of potential fields geometric method and reduced euler deconvolution a new method based on 3d multiridge analysis of potential fields assumes a 3d subset in the harmonic region and studies the behavior of potential field ridges which are built by joining extreme points of the analyzed field computed at different altitudes three types of ridges are formed by searching for the zeros of the first horizontal and first vertical derivatives of the potential field types i and ii respectively and the zeros of the potential field itself type iii this method uses a redundant set of ridges called a multiridge set to determine source type and location for homogeneous potential fields generated by simple sources all of the ridges are straight lines converging to the source position this method analyzes the multiridges by using a geometric criterion to find the source position at the intersection of the multiridge set and by solving the three reduced euler equations associated with ridge types i ii and iii the reduced euler type i and ii equations are used to obtain the structural index and the vertical and horizontal source positions equation type iii estimates the horizontal and vertical source positions tests on synthetic as well as the bishop model field yield good results even with noise corrupted data results obtained using magnetic data collected over the wreck of a military ship in the tyrrhenian sea successfully determine its vertical and horizontal positions and the structural index

hypergeometric type differential equations second kind solutions and related integrals a rodrigues type representation for the second kind solutions of a second order differential equation of hypergeometric type is given this representation contains some integrals related with relevant special functions for these integrals a general recurrence relation which only involves the coefficients of the differential equation is also presented finally an extension of the rodrigues type representation for the second solution of a second order difference equation of hypergeometric type is indicated

magsounddst 3d automatic inversion of magnetic and gravity data based on the differential similarity transform we present an automatic procedure magnetic and gravity sounding differential similarity transformmagsounddst for inversion of regular or irregular magnetic and gravitygrid data measured on even or uneven surfaces it solves for horizontal position depth and structural index of simple sources and is independent of a linear background in addition it estimates the shape of sources consisting of several singular points and lines the method uses the property of the differential similarity transform dst of a magnetic or a gravity anomaly to become zero or linear at all observation points when the central point of similarity of the transform which we refer to as the probing point coincides with a source s singular point it uses a measured anomalous field and its calculated or measured gradiometry first order derivatives the method is independent of the magnetization vector direction in the magnetic data case and does not require reduction to the pole transformed data as input with magsounddst we provide an important alternative interpretation technique to the euler deconvolution procedures combining a moving window method whereby the solutions are linked to singular points of causative bodies with an approach in which the solutions are linked to the real sources the procedure involves calculating a 3d function that evaluates the linearity of the dst for different integer or noninteger structural indices using a moving window we sound the subsurface along a vertical line under each window center then we combine the 3d results for different structural indices and present them in three easy tointerpret maps avoiding the need for clustering techniques we deduce only one solution for location and type of simple sources which is a major advantage over euler deconvolution application to different cases of synthetic and real data shows the method s applicability to various types of magnetic and gravity field investigations

hierarchy of stability criterion for time delay systems based on multiple integral approach abstract taking a class of time delay systems as research object this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free weighting matrix technique the hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in lyapunov krasovskii functional lkf together with three numerical experiments the hierarchy of stability criterion is further shown

automatic inversion of magnetic anomalies from two height levels using finite difference similarity transforms we solve the inverse magnetic problem for the depth and shape of simple sources in the presence of a regional field and truly random noise we do not use noise generating derivatives nor are we forced to solve complex systems of equations our inverse operator applies a new geometric type of field transform the finite difference similarity transform fdst that is based on a postulated degree of homogeneity in the potential field magnetic data from two height levels are required for the calculation of the fdsts the fdsts are generated for an assumed central point of similarity cps and a trial value index for the coefficient of similarity and they are sensitive to the distance between the source and the cps and to the agreement between the index and the degree of homogeneity in the data when the cps converges to a singular point in the potential field say the center or the topedge of the source and when the trial index converges on the degree of homogeneity present in the data the fdst drops

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities