the existence of subspace wavelet sets let h be a reducing subspace of l2 rd that is a closed subspace of l2 rd with the property that f amt l h for any f h m z and l zd where a is a d d expansive matrix it is known that h is a reducing subspace if and only if there exists a measurable subset m of rd such that atm m and f h l2 rd m under some given conditions of m it is known that there exist a dilation subspace wavelet sets iwith respect to h in this paper we prove that this holds in general

input to state stabilization of nonlinear discrete time systems with event triggered controllers abstract this paper studies an event triggered control problem of nonlinear discrete time systems in the presence of external disturbances in particular we focus on the practically interesting situation where the controller update at step k is determined by the feedback information x k 1 measured at step k 1 the presence of external disturbance makes it hard to predict the magnitude of x k based on x k 1 and then to design a desired event triggering data transmission mechanism in this paper refined tools of input to state stability iss and the nonlinear small gain theorem are developed to estimate the influence of external disturbances before an iss induced design is proposed to solve the problem the proposed solution leads to a new event triggering data transmission mechanism which drastically differs from the existing event triggered control results

efficiently attentive event triggered systems with limited bandwidth event triggered systems sample and transmit data when a state dependent criterion is violated many event triggered systems are efficiently attentive i e longer inter sampling intervals are achieved as the system gets closer to its equilibrium this property allows event triggered systems to use fewer communication resources since control systems are usually operated around their equilibria efficient attentiveness however is not a necessary property of all event triggered systems to ensure efficient attentiveness this technical note proposes an approach to design event triggers and quantization maps for nonlinear systems with transmission delays we present sufficient conditions to guarantee input to state stability iss of the resulting systems without exhibiting zeno behavior

lyapunov formulation of the large scale iss cyclic small gain theorem the discrete time case abstract this paper presents a lyapunov formulation of the cyclic small gain theorem for dynamical networks composed of discrete time input to state stable iss subsystems iss lyapunov functions for dynamical networks satisfying the cyclic small gain condition are constructed from the iss lyapunov functions of the subsystems

robust input to state stability for hybrid systems this work addresses input to state stability iss for hybrid dynamical systems which combine continuous time dynamics on a flow set and discrete time dynamics on a jump set the main result entails equivalent characterizations of iss when the right hand side of the differential equation for the continuous time dynamics is locally lipschitz but the set of admissible derivative values generated by considering all possible input values is not necessarily convex under some mild assumptions we show that existence of an iss lyapunov function is equivalent to various types of robust iss for these hybrid systems as an application we demonstrate how a hybrid system framework can be used to study some stability properties for continuous time systems in particular we use the derived equivalent characterization results of iss for hybrid systems to recover and generalize lyapunov and asymptotic characterizations of input output to state stability for continuous time systems

3d symmetry detection using the extended gaussian image symmetry detection is important in the area of computer vision a 3d symmetry detection algorithm is presented in this paper the symmetry detection problem is converted to the correlation of the gaussian image once the gaussian image of the object has been obtained the algorithm is independent of the input format the algorithm can handle different kinds of images or objects simulated and real images have been tested in a variety of formats and the results show that the symmetry can be determined using the gaussian image

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

wavelet frames for not necessarily reducing affine subspaces ii the structure of affine subspaces abstract this is a continuation of the investigation into the theory of wavelet frames for general affine subspaces the main focus of this paper is on the structural properties of affine subspaces we show that every affine subspace is the orthogonal direct sum of at most three purely non reducing subspaces while every reducing subspace with respect to the dilation and translation operators is the orthogonal direct sum of two purely non reducing ones this result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine motivated by the fundamental question as to whether every affine subspace is singly generated and by a recent result that every singly generated purely non reducing subspace admits a singly generated wavelet frame we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of small size as a consequence we establish a connection between the above mentioned two questions

on input to state stability of discrete time switched nonlinear time varying systems in this paper input to state stability iss for discrete time switched nonlinear time varying sntv systems is investigated starting with discrete time nonlinear time varying ntv systems some improved sufficient conditions are proposed to verify the iss of systems by using the weak implication form iss wi iss lyapunov function weak dissipative form iss wd iss lyapunov function and interval descent technique then the results obtained are extended to study the iss of discrete time sntv systems several relaxed conditions are given by using piecewise wi iss and wd iss lyapunov functions minimum dwell time and infinite switching methods respectively comparing with the existing results the obtained conditions release the requirement on negative definiteness of the differences of piecewise lyapunov functions moreover all subsystems are allowed to be unstable in the case of infinite switching finally a numerical example is given to illustrate the theoretical results

the structure of shift invariant subspaces of l2 rn using the range function approach to shift invariant spaces in l2 rn we give a simple characterization of frames and riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l2 zn this in turn gives a simplified approach to the analysis of frames and riesz families done by gramians and dual gramians we prove a decomposition of a shift invariant space into the orthogonal sum of spaces each of which is generated by a quasi orthogonal generator as an application of this fact we characterize shift preserving operators in terms of range operators and prove some facts about the dimension function

panorama a 3d shape descriptor based on panoramic views for unsupervised 3d object retrieval we present a novel 3d shape descriptor that uses a set of panoramic views of a 3d object which describe the position and orientation of the object s surface in 3d space we obtain a panoramic view of a 3d object by projecting it to the lateral surface of a cylinder parallel to one of its three principal axes and centered at the centroid of the object the object is projected to three perpendicular cylinders each one aligned with one of its principal axes in order to capture the global shape of the object for each projection we compute the corresponding 2d discrete fourier transform as well as 2d discrete wavelet transform we further increase the retrieval performance by employing a local unsupervised relevance feedback technique that shifts the descriptor of an object closer to its cluster centroid in feature space the effectiveness of the proposed 3d object retrieval methodology is demonstrated via an extensive consistent evaluation in standard benchmarks that clearly shows better performance against state of the art 3d object retrieval methods

lyapunov based small gain theorems for hybrid systems constructions of strong and weak lyapunov functions are presented for a feedback connection of two hybrid systems satisfying certain lyapunov stability assumptions and a small gain condition the constructed strong lyapunov functions can be used to conclude input to state stability iss of hybrid systems with inputs and global asymptotic stability gas of hybrid systems without inputs in the absence of inputs we also construct weak lyapunov functions nondecreasing along solutions and develop a lasalle type theorem providing a set of sufficient conditions under which such functions can be used to conclude gas in some situations we show how average dwell time adt and reverse average dwell time radt clocks can be used to construct lyapunov functions that satisfy the assumptions of our main results the utility of these results is demonstrated for the natural decomposition of a hybrid system as a feedback connection of its continuous and discrete dynamics and in several design oriented contexts networked control systems event triggered control and quantized feedback control

small gain theorems for large scale systems and construction of iss lyapunov functions we consider interconnections of n nonlinear subsystems in the input to state stability iss framework for each subsystem an iss lyapunov function is given that treats the other subsystems as independent inputs a gain matrix is used to encode the mutual dependencies of the systems in the network under a small gain assumption on the monotone operator induced by the gain matrix a locally lipschitz continuous iss lyapunov function is obtained constructively for the entire network by appropriately scaling the individual lyapunov functions for the subsystems the results are obtained in a general formulation of iss the cases of summation maximization and separation with respect to external gains are obtained as corollaries

triangular wavelet based finite elements via multivalued scaling equations this paper develops a class of triangular finite elements based on l2 rn orthonormal compactly supported wavelets as in the case of recently derived tensor product wavelet elements the triangular elements are defined by deriving an algebraic eigenvalue problem characterizing the entries of the elemental matrices these entries are uniquely defined by normalization conditions derived from the polynomial reproducing properties of the wavelet scaling functions the work herein generalizes the development of the tensor product wavelet elements in that the geometry of the triangular elemental domain is characterized using a multivalued scaling equation the multivalued scaling function is used to represent the self similar tiling of rn onto itself by triangular domains

relaxed conditions for the input to state stability of switched nonlinear time varying systems this technical note considers the problem of input to state stability iss for switched nonlinear time varying systems first a sufficient condition is proposed to verify the iss of nonlinear time varying systems by using an improved lyapunov function then the results obtained are extended to study the iss of switched nonlinear time varying systems three relaxed conditions are given by using the methods of multiple lyapunov functions minimum dwell time and infinite switchings respectively comparing with the existing results the conditions obtained have two relaxations i e the derivative of lyapunov functions of subsystems are allowed to be indefinite and all subsystems are allowed to be unstable in the case of infinite switchings all results obtained also be used to study the uniformly asymptotic stability uas of systems finally a numerical example is given to illustrate the theoretical results

input to state stability of interconnected hybrid systems we consider the interconnections of arbitrary topology of a finite number of iss hybrid systems and study whether the iss property is maintained for the overall system we show that if the small gain condition is satisfied then the whole network is iss and show how a non smooth iss lyapunov function can be explicitly constructed in this case

the structure of finitely generated shift invariant spaces in l2 rd a simple characterization is given of finitely generated subspaces of l2 rd which are invariant under translation by any multi integer and is used to give conditions under which such a space has a particularly nice generating set namely a basis and more than that a basis with desirable properties such as stability orthogonality or linear independence the last property makes sense only for local spaces i e shift invariant spaces generated by finitely many compactly supported functions and special attention is paid to such spaces as an application we prove that the approximation order provided by a given local space is already provided by the shift invariant space generated by just one function with this function constructible as a finite linear combination of the finite generating set for the whole space hence compactly supported this settles a question of some 20 years standing

characterizations of input to state stability for hybrid systems abstract we study input to state stability iss for a broad class of hybrid systems which are combinations of a differential equation on a constraint set and a difference equation on another constraint set for this class of hybrid systems we establish the equivalence of iss nonuniform iss and the existence of a smooth iss lyapunov function by additionally assuming that the right hand side of the differential equation has a convex property with respect to inputs moreover we demonstrate by examples that the equivalence may fail when such a convexity assumption is removed

uniform input to state stability for switched and time varying impulsive systems we provide a lyapunov function based method for establishing different types of uniform input to state stability iss for time varying impulsive systems the method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the lyapunov function on the system trajectories this reduction is performed in such a way that the resulting scalar system has no inputs novel sufficient conditions for iss are provided which generalize existing results for time invariant and time varying switched and nonswitched impulsive and nonimpulsive systems in several directions

multiple lyapunov functions based small gain theorems for switched interconnected nonlinear systems multiple lyapunov functions mlfs based small gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems which extend the small gain technique from its original non switched nonlinear version to a switched nonlinear version each low dimensional subsystem does not necessarily have the input to state stability iss property in the whole state space and it only has individual iss property in some subregions of the state space the novelty of this paper is that integral type mlfs and small gain techniques are utilized to establish some mlfs based small gain theorems for switched interconnected nonlinear systems which derive various stability results under some novel switching laws designed and construct integral type mlfs the small gain theorems proposed cover several recent results as special cases which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are iss or only some are iss and others are not finally two illustrative examples are presented to demonstrate the effectiveness of the results provided

small gain based output feedback controller design for a class of nonlinear systems with actuator dynamic quantization this technical note presents a novel recursive design approach for output feedback control of a class of nonlinear systems with actuator quantization the recently developed cyclic small gain theorem is employed to guarantee the input to state stability iss of the closed loop system along with the construction of an iss lyapunov function actuator dynamic quantization is designed based on the iss lyapunov function

efficient 3d shape matching and retrieval using a concrete radialized spherical projection representation we present a 3d shape retrieval methodology based on the theory of spherical harmonics using properties of spherical harmonics scaling and axial flipping invariance is achieved rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies pca on the face normals of the model the 3d model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point the superior performance of the proposed methodology is demonstrated through a comparison against state of the art approaches on standard databases

rosy 3d object pose normalization based on pca and reflective object symmetry with application in 3d object retrieval a novel pose normalization method based on 3d object reflective symmetry is presented it is a general purpose global pose normalization method in this paper it is used to enhance the performance of a 3d object retrieval pipeline initially the axis aligned minimum bounding box of a rigid 3d object is modified by requiring that the 3d object is also in minimum angular difference with respect to the normals to the faces of its bounding box to estimate the modified axis aligned bounding box a set of predefined planes of symmetry are used and a combined spatial and angular distance between the 3d object and its symmetric object is calculated by minimizing the combined distance the 3d object fits inside its modified axis aligned bounding box and alignment with the coordinate system is achieved the proposed method is incorporated in a hybrid scheme that serves as the alignment method in a 3d object retrieval system the effectiveness of the 3d object retrieval system using the hybrid pose normalization scheme is evaluated in terms of retrieval accuracy and demonstrated using both quantitative and qualitative measures via an extensive consistent evaluation on standard benchmarks the results clearly show performance boost against current approaches

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

an approximate and efficient method for optimal rotation alignment of 3d models in many shape analysis applications the ability to find the best rotation that aligns two models is an essential first step in the analysis process in the past methods for model alignment have either used normalization techniques such as pca alignment or have performed an exhaustive search over the space of rotation to find the best optimal alignment while normalization techniques have the advantage of efficiency providing a quick method for registering two shapes they are often imprecise and can give rise to poor alignments conversely exhaustive search is guaranteed to provide the correct answer but even using efficient signal processing techniques this type of approach can be prohibitively slow in this paper we present a new method for aligning two 3d shapes we show that the method is markedly faster than existing approaches based on efficient signal processing and we provide registration results demonstrating that the alignments obtained using our method have a high degree of precision and are markedly better than those obtained using normalization

discrete time lyapunov based small gain theorem for parameterized interconnected iss systems input to state stability iss of a feedback interconnection of two discrete time iss systems satisfying an appropriate small gain condition is investigated via the lyapunov method in particular an iss lyapunov function for the overall system is constructed from the iss lyapunov functions of the two subsystems we consider parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used in controller design for a sampled data system

a lyapunov proof of an improved maximum allowable transfer interval for networked control systems simple lyapunov proofs are given for an improved relative to previous results that have appeared in the literature bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval

smooth lyapunov functions for hybrid systems part ii pre asymptotically stable compact sets it is shown that pre asymptotic stability which generalizes asymptotic stability of a compact set for a hybrid system satisfying mild regularity assumptions is equivalent to the existence of a smooth lyapunov function this result is achieved with the intermediate result that asymptotic stability of a compact set for a hybrid system is generically robust to small state dependent perturbations as a special case we state a converse lyapunov theorem for systems with logic variables and use this result to establish input to state stabilization using hybrid feedback control the converse lyapunov theorems are also used to establish semiglobal practical robustness to slowly varying weakly jumping parameters to temporal regularization to the insertion of jumps according to an ldquoaverage dwell timerdquo rule and to the insertion of flow according to a ldquoreverse average dwell timerdquo rule

rectilinearity of 3d meshes in this paper we propose and evaluate a novel shape measure describing the extent to which a 3d polygon mesh is rectilinear the rectilinearity measure is based on the maximum ratio of the surface area to the sum of three orthogonal projected areas of the mesh it has the following desirable properties 1 the estimated rectilinearity is always a number from 0 1 2 the measure is invariant under scale rotation and translation 3 the 3d objects can be either open or closed meshes and we can also deal with degenerate meshes 4 the measure is insensitive to noise stable under small topology errors and robust against face deletion and mesh simplification moreover a genetic algorithm ga can be applied to compute the approximate rectilinearity efficiently we find that the calculation of rectilinearity can be used to normalize the pose of 3d meshes and in many cases it performs better than the principal component analysis pca based method by applying a simple selection criterion the combination of these two methods results in a new pose normalization algorithm which not only provides a higher successful alignment rate but also corresponds better with intuition finally we carry out several experiments showing that both the rectilinearity based pose normalization preprocessing and the combined signatures which consist of the rectilinearity measure and other shape descriptors can significantly improve the performance of 3d shape retrieval

u invariant sampling and reconstruction in atomic spaces with multiple generators given a u invariant sampling scheme on a hilbert space h this paper characterizes atomic subspaces a of h such that every signal x a can be reconstructed from its generalized samples acquired with the u invariant sampling scheme if signal recovery is possible a linear filter is derived which reconstructs the signal from the samples moreover the paper gives necessary and sufficient conditions on a sequence of sampling functions such that it forms a pseudoframe or pseudo riesz basis for a given atomic subspace a

strong iss implies strong iiss for time varying impulsive systems abstract for time invariant nonimpulsive systems it is already well known that the input to state stability iss property is strictly stronger than integral input to state stability iiss very recently we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics iss implies iiss also for time varying systems in this paper we show that this implication remains true for impulsive systems provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems

the structure of shift modulation invariant spaces the rational case in this paper we study structural properties of shift modulation invariant smi spaces also called gabor subspaces or weyl heisenberg subspaces in the case when shift and modulation lattices are rationally dependent we prove the characterization of smi spaces in terms of range functions analogous to the well known description of shift invariant spaces c de boor r devore a ron the structure of finitely generated shift invariant spaces in l2 r d j funct anal 119 1994 37 78 m bownik the structure of shift invariant subspaces of l2 r n j funct anal 177 2000 282 309 h helson lectures on invariant subspaces academic press new york london 1964 we also give a simple characterization of frames and riesz sequences in terms on their behavior of the fibers of the range function next we prove several orthogonal decomposition results of smi spaces into simpler blocks called principal smi spaces then this is used to characterize operators invariant under both shifts and modulations in terms of families of linear maps acting on the fibers of the range function we also introduce the fundamental concept of the dimension function for smi spaces as a result this leads to the classification of unitarily equivalent smi spaces in terms of their dimension functions finally we show several results illustrating our fiberization techniques to characterize dual gabor frames

a region dependent gain condition for asymptotic stability a sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem roughly speaking to apply this theorem it is required that the gains composition is continuous increasing and upper bounded by the identity function in this work an alternative sufficient condition is presented for the case in which this criterion fails due to either lack of continuity or the bound of the composed gain is larger than the identity function more precisely the local resp non local asymptotic stability of the origin resp global attractivity of a compact set is ensured by a region dependent small gain condition under an additional condition that implies convergence of solutions for almost all initial conditions in a suitable domain the almost global asymptotic stability of the origin is ensured two examples illustrate and motivate this approach

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

a lyapunov based small gain theorem for interconnected switched systems abstract stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input to state stable non iss we show that providing the switching signals neither switch too frequently nor activate non iss subsystems for too long a small gain theorem can be used to conclude global asymptotic stability gas of the interconnected system for each switched system with the constraints on the switching signal being modeled by an auxiliary timer a correspondent hybrid system is defined to enable the construction of a hybrid iss lyapunov function apart from justifying the iss property of their corresponding switched systems these hybrid iss lyapunov functions are then combined to establish a lyapunov type small gain condition which guarantees that the interconnected system is globally asymptotically stable

symmetry identification of a 3 d object represented by octree an algorithm for identifying symmetry of a 3 d object given by its octree is presented and the symmetry degree a measure of object symmetry is proposed the algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree an object can be in an arbitrary position and with arbitrary orientation within the octree space and a wide range of symmetries represented by groups of proper and improper rotations can be identified it is shown that the octree data structure supports these operations well especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry the operation of the algorithm is illustrated using some synthetic test objects the results which are composed of identified symmetry types and the corresponding symmetry degrees were satisfactory