output feedback stabilization of nonlinear dual rate sampled data systems via an approximate discrete time model the problem of output feedback stabilization of nonlinear sampled data control systems is considered under the low measurement rate constraint a dual rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the missing output values between measured output samples it is shown that if an observer based output feedback controller that semiglobally practically asymptotically spa stabilizes the single rate sampled data plant model is given then the spa stability property will be preserved for the closed loop dual rate sampled data system on the basis of the proposed dual rate control scheme under standard assumptions a numerical example is given to illustrate the design method

ricci collineations of static spherically symmetric spacetimes the ricci collineations of static spherically symmetric spacetimes are classified and their relationship with isometries is discussed a general theorem about this relationship is stated and its extension to all spherically symmetric spacetimes is discussed

input to state stability for discrete time time varying systems with applications to robust stabilization of systems in power form input to state stability iss of a parameterized family of discrete time time varying nonlinear systems is investigated a converse lyapunov theorem for such systems is developed we consider parameterized families of discrete time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete time model is used to design a controller for a sampled data system an application of our main result to time varying periodic systems is presented and this is used to solve a robust stabilization problem namely to design a control law for systems in power form yielding semiglobal practical iss sp iss

classification of spherically symmetric static space times by their curvature collineations a complete classification of all spherically symmetric static space times according to their curvature collineations is presented and compared with ricci collineations of corresponding space times

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

changing supply rates for input output to state stable discrete time nonlinear systems with applications we present results on changing supply rates for input output to state stable discrete time nonlinear systems our results can be used to combine two lyapunov functions none of which can be used to verify that the system has a certain property into a new composite lyapunov function from which the property of interest can be concluded the results are stated for parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used to design a controller for a sampled data system we present several applications of our results i a lasalle criterion for input to state stability iss of discrete time systems ii constructing iss lyapunov functions for time varying discrete time cascaded systems iii testing iss of discrete time systems using positive semidefinite lyapunov functions iv observer based input to state stabilization of discrete time systems our results are exploited in a case study of a two link manipulator and some simulation results that illustrate advantages of our approach are presented

mastersymmetries angle variables and recursion operator of the relativistic toda lattice conserved quantities bi hamiltonian formulation and recursive structure of the relativistic toda lattice rt are obtained in an algorithmic way without making use of the lax representation furthermore for the multisoliton solutions the gradients of the angle variables are described in terms of mastersymmetries a new hierarchy of completely integrable systems is discovered which turns out to correspond to the negative of the hierarchy of rt thus it is shown that the full algebra of time dependent symmetry group generators for each member of the rt hierarchy is isomorphic to the algebra of first order differential operators with laurent polynomials as coefficients the surprising phenomenon is revealed that the members of the rt hierarchy are connected to their negative counterparts by explicit backlund transformation

killing vectors of static spherically symmetric metrics an error in a previous theorem j math phys 28 1019 1987 29 525 1988 is corrected and the theorem is extended

symmetries of the energy momentum tensor of cylindrically symmetric static space times we investigate matter symmetries of cylindrically symmetric static space times these are classified for both cases when the energy momentum tensor is nondegenerate and also when it is degenerate it is found that the nondegenerate energy momentum tensor gives either three four five six seven or ten independent matter collineations in which three are isometries and the rest are proper the worth mentioning cases are those where we obtain the group of matter collineations finite dimensional even the energy momentum tensor is degenerate these are either three four five or ten some examples are constructed satisfying the constraints on the energy momentum tensor

joint mr pet reconstruction using a multi channel image regularizer while current state of the art mr pet scanners enable simultaneous mr and pet measurements the acquired data sets are still usually reconstructed separately we propose a new multi modality reconstruction framework using second order total generalized variation tgv as a dedicated multi channel regularization functional that jointly reconstructs images from both modalities in this way information about the underlying anatomy is shared during the image reconstruction process while unique differences are preserved results from numerical simulations and in vivo experiments using a range of accelerated mr acquisitions and different mr image contrasts demonstrate improved pet image quality resolution and quantitative accuracy

examples of signature 2 2 manifolds with commuting curvature operators we exhibit walker manifolds of signature 2 2 with various commutativity properties for the ricci operator the skew symmetric curvature operator and the jacobi operator if the walker metric is a riemannian extension of an underlying affine structure these properties are related to the ricci tensor of

brief paper continuous time controller redesign for digital implementation a trajectory based approach given a continuous time nonlinear closed loop system we investigate sampled data feedback laws for which the trajectories of the sampled data closed loop system converge to the continuous time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero we derive necessary and sufficient conditions for the existence of such sampled data feedback laws and in case of existence provide explicit redesign formulas and algorithms for these controllers

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

affine collineations in space time the existence of affine collineations in space time is discussed and the types of space time admitting proper affine collineations is displayed the close connection between such space times and their holonomy structure and local decomposability is established affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space time

further results on robustness of possibly discontinuous sample and hold feedback we demonstrate that sample and hold state feedback control possibly discontinuous with respect to the state is robust when the closed loop system possesses an appropriate lyapunov function we first show that if a lyapunov decrease over sampling periods exists for the nominal system this decrease can be maintained with some degradation relative to a sufficiently small additive perturbation we then proceed to catalog several applications of this robustness e g robustness to measurement noise computational delays or fast actuator dynamics

covariantly constant tensors and holonomy structure in general relativity this paper attempts to give a comprehensive discussion of space times that admit vector fields or second order symmetric or skew symmetric tensor fields which are covariantly constant or recurrent the relationship between such space times m and their holonomy group is given

technical communique robust backstepping for the euler approximate model of sampled data strict feedback systems stabilization of uncertain sampled data strict feedback systems is addressed the stability study is carried out on the euler approximation of the exact discretized model of the plant firstly a class of state feedback controllers is developed that guarantees an input to state stability property for the closed loop system additionally assuming some hypotheses on the uncertain terms hold a practical asymptotic stability property is ensured by designing an appropriate class of controllers

affine conformal vectors in space time all space times admitting a proper affine conformal vector acv are found by using a theorem of hall and da costa it is shown that such space times either i admit a covariantly constant vector timelike spacelike or null and the acv is the sum of a proper affine vector and a conformal killing vector or ii the space time is 2 2 decomposable in which case it is shown that no acv can exist unless the space time decomposes further furthermore it is proved that all space times admitting an acv and a null covariantly constant vector which are necessarily generalized pp wave space times must have ricci tensor of segre type 2 1 1 it follows that among space times admitting proper acv the einstein static universe is the only perfect fluid space time there are no non null einstein maxwell space times and only the pp wave space times are representative of null einstein maxwell solutions otherwise the space times can represent anisotropic fluids and viscous heat conducting fluids but only with restricted equations of state in each case

an example of affine collineation in the robertson walker metric an affine collineation for the robertson walker metric is found it implies a condition on the metric that is compatible with einstein s equations for a perfect fluid satisfying the hawking ellis energy conditions it is shown how the geodesics of the metric are obtained from the constant of motion associated to the affine collineation

ricci collineation vectors in fluid space times the properties of fluid space times that admit a ricci collineation vector rcv parallel to the fluid unit four velocity vector ua are briefly reviewed these properties are expressed in terms of the kinematic quantities of the timelike congruence generated by ua the cubic equation derived by oliver and davis ann inst henri poincare 30 339 1979 for the equation of state p p of a perfect fluid space time that admits an rcv which does not degenerate to a killing vector is solved for physically realistic fluids necessary and sufficient conditions for a fluid space time to admit a spacelike rcv parallel to a unit vector na orthogonal to ua are derived in terms of the expansion shear and rotation of the spacelike congruence generated by na perfect fluid space times are studied in detail and analogues of the results for timelike rcvs parallel to ua are obtained properties of imperfect fluid space times for which the energy flux vector qa vanishes and na is a spacelike eigenvector of the aniso

incorporation of space time symmetries in einstein s field equations in the search for exact solutions to einstein s field equations the main simplification tool is the introduction of space time symmetries motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry the method is being expressed in a covariant formalism using the framework of a double congruence the basic notion on which it is based is that of the geometrization of a general symmetry as a special application of our general method we consider the case of a space like conformal killing vector field on the space time manifold regarding special types of matter fields new perspectives in general relativity are discussed

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

backstepping designs for the stabilisation of nonlinear sampled data systems via approximate discrete time model the problems of backstepping adaptive backstepping and reduced order observer based output feedback control of sampled data nonlinear systems in strict feedback form are considered controller design methods based on the euler approximate model are presented for these problems the controllers are designed to compensate the effects of the discrepancy between the euler approximate model and exact discrete time model parameter estimation error in adaptive control and observer error in output feedback control which behave as disturbance it is shown that the obtained controllers semi globally practically asymptotically stabilise the plant model under standard assumptions then numerical examples are given to illustrate the design methods

stabilization of sampled data nonlinear systems via backstepping on their euler approximate model two integrator backstepping designs are presented for digitally controlled continuous time plants in special form the controller designs are based on the euler approximate discrete time model of the plant and the obtained control algorithms are novel the two control laws yield respectively semiglobal practical stabilization and global asymptotic stabilization of the euler model both designs achieve semiglobal practical stabilization in the sampling period that is regarded as a design parameter of the closed loop sampled data system a simulation example illustrates that the obtained controllers may sometimes be superior to backstepping controllers based on the continuous time plant model that are implemented digitally

collineations of a symmetric 2 covariant tensor ricci collineations the infinitesimal transformations that leave invariant a two covariant symmetric tensor are studied the interest of these symmetry transformations lays in the fact that this class of tensors includes the energy momentum and ricci tensors we find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional lie algebra but in some cases exhibiting a higher degree of degeneracy this class is infinite dimensional and may fail to be a lie algebra as an application we study the ricci collineations of a type b warped spacetime

backstepping control under multi rate sampling the paper deals with the design of sampled data controllers which preserve the stabilizing performance of a continuous time backstepping control strategy this is achieved through matching of the control lyapunov functions evolutions at the sampling instants the method is developed for systems in strict feedback form the results are discussed and compared with similar strategies through simulated examples

curvature structure in general relativity this paper investigates the extent to which the curvature structure of space time determines the metric stucture it continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders it is shown that with the exception of the so called generalized pp waves the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations

holonomy groups in general relativity the infinitesimal holonomy group structure of space time is discussed and related to the petrov type of the weyl tensor and the algebraic segre type of the energy momentum tensor the number of covariant derivatives of the curvature tensor required to determine the infinitesimal holonomy group is determined in each case and the complete classification scheme is tabulated some special cases of physical interest are investigated in more detail a geometrical approach is followed throughout

affine collineations in general relativity and their fixed point structure a general discussion of affine vector fields collineations in space time is given following a previous article by hall and da costa some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established some preliminary results regarding homothetic symmetries in two and three dimensional space times are also given the impossibility of reducing an affine algebra containing proper affine vector fields to homothetic or killing vector fields by means of a change of compatible metric is demonstrated

the ricci soliton equation and the structure of homogeneous godel type spacetimes abstract we completely determine the solutions to the ricci soliton equation among homogeneous godel type metrics investigating the properties of these solutions we also obtain some new insights on the structure of these spacetimes

spacetimes admitting a vector field whose inner product with the riemann tensor is zero the equation v r 0 arises in various places in general relativity in particular as the integrability conditions of the equations lvg 2 g where is a constant these are the equations of a homothetic vector field v with a zero homothetic bivector dv 0 in some space time with metric g and r are the components of the riemann tensor of that metric in some frame in this paper the equation v r 0 is examined and the components of the riemann tensor for the spacetimes which admit nonzero solutions v of this equation are given the petrov types of the weyl tensors of these spacetimes are listed and as a result a correction is then made to a theorem in a paper by collinson and fugere about the petrov types of spacetimes which admit the type of separation that they require of the hamilton jacobi equation for these spacetimes

affine collineations in riemannian spaces sufficient conditions on the christoffel symbols and metric tensors to insure the existence of affine collineations in riemann spaces are obtained a proof of the group property of affine collineations is given several examples of physically relevant riemannian spaces admitting affine collineations are presented and the constants of motion are constructed

collineations of godel type space times ricci collineations for godel type space times are studied the members of this family of metrics admitting these symmetries are identified it is shown that these space times do not admit homothetic vector fields also the unique affine collineation associated to godel type space times is exhibited

vector valued image processing by parallel level sets vector valued images such as rgb color images or multimodal medical images show a strong interchannel correlation which is not exploited by most image processing tools we propose a new notion of treating vector valued images which is based on the angle between the spatial gradients of their channels through minimizing a cost functional that penalizes large angles images with parallel level sets can be obtained after formally introducing this idea and the corresponding cost functionals we discuss their gateaux derivatives that lead to a diffusion like gradient descent scheme we illustrate the properties of this cost functional by several examples in denoising and demosaicking of rgb color images they show that parallel level sets are a suitable concept for color image enhancement demosaicking with parallel level sets gives visually perfect results for low noise levels furthermore the proposed functional yields sharper images than the other approaches in comparison

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

geometrization of a general collineation geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities shear vorticity expansion of the congruence of the vector field generating the collineation it is shown that the generic form of a collineation is l gab 2 gab hab where hab is a traceless symmetric tensor a general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed

curvature collineations in general relativity ii this paper is the second of a set of two papers on curvature collineations in general relativity the first paper presented the mathematical basis of curvature collineations and a possible approach to their study this paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space time it is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here this together with the geometrical approach favored in this paper leads to a rather general discussion of the problem which it is hoped does not obscure those physical aspects of the situation that are important in einstein s theory

contrast invariant snr and isotonic regressions we design an image quality measure independent of contrast changes which are defined as a set of transformations preserving an order between the level lines of an image this problem can be expressed as an isotonic regression problem depending on the definition of a level line the partial order between adjacent regions can be defined through chains polytrees or directed acyclic graphs we provide a few analytic properties of the minimizers and design original optimization procedures together with a full complexity analysis the methods worst case complexities range from o n for chains to o n log n for polytrees and o frac n 2 sqrt epsilon for directed acyclic graphs where n is the number of pixels and epsilon is a relative precision the proposed algorithms have potential applications in change detection stereo vision image registration color image processing or image fusion a c implementation with matlab headers is available at https github com pierre weiss contrast invariant snr

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

collineations of the ricci tensor ricci collineations for the ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of rab r such that rab 0 for a b it turns out that the only collineations admitted by this tensor can be ten six or four and there does not appear any case in between

curvature inheritance symmetry in riemannian spaces with applications to fluid space times katzin et al g h katzin j levine and w r davis j math phys 10 617 1969 introduced curvature collineations cc defined by a vector satisfying l rbcda 0 where rbcda is the riemann curvature tensor of a riemannian space vn and l denotes the lie derivative they proved that a cc is related to a special conformal motion which implies the existence of a covariant constant vector field unfortunately recent study indicates that the existence of a covariant constant vector restricts vn to a very rare special case with limited physical use in particular for a fluid space time with special conformal motion either stiff or unphysical equations of state are singled out moreover perfect fluid space times do not admit special conformal motions this information was not available in 1969 when cc symmetry was introduced in this paper cc is generalized to another symmetry called curvature inheritance ci satisfying l rbcda 2 rbcda where is a scalar function we prove that a proper

spacelike conformal killing vectors and spacelike congruences necessary and sufficient conditions are derived for space time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na these conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four velocity of the observer employed at any given point of the congruence it is shown that either the expansion or the rotation of this spacelike congruence must vanish if dna dp 0 where p denotes arc length measured along the integral curves of na and also that there exist no proper spacelike homothetic motions with constant expansion propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid fluid space times are studied in detail a relation is established between spacelike conformal motions and material curves in the fluid if a fluid space time admits a spacelike conformal killing vector parallel to na and

geodesic first integrals with explicit path parameter dependence in riemannian space times in a riemannian space vn general formulas are obtained for geodesic first integrals which are mth order polynomials in the tangent vector and which are assumed to depend explicitly on the path parameter s it is found that such first integrals must also be polynomials in s necessary and sufficient conditions are found for the existence of these first integrals the existence of many well known symmetries such as homothetic motions scale change affine collineations conformal motions projective collineations conformal collineations or special curvature collineations are shown to be sufficient for the existence of such first integrals with explicit path parameter dependence to illustrate the theory geodesic first integrals of this type have been calculated for four riemannian space times of general relativity