discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

a variational iterative technique applied to quantum mechanical problems a technique for solving nonlinear operator equations iteratively is applied to quantum mechanical calculations it is shown that alternative methods of applying the technique lead to another way of approaching variational calculations and generalisations of perturbation theory respectively

technical communique optimally switched linear systems in this paper we address the problem of optimal switching for switched linear systems the uniqueness of our approach lies in describing the switching action by multiple control inputs this allows us to embed the switched system in a larger family of systems and apply pontryagin s minimum principle for solving the optimal control problem this approach imposes no restriction on the switching sequence or the number of switchings this is in contrast to search based algorithms where a fixed number of switchings is set a priori in our approach the optimal solution can be determined by solving the ensuing two point boundary value problem results of numerical simulations are provided to support the proposed method

ℋ stabilisation of switched linear stochastic systems under dwell time constraints based on the determination of a minimum dwell time this article addresses the problem of characterising a switching strategy for stabilisation of switched linear stochastic systems with adapted external inputs sufficient conditions that assure exponential mean square stability and an performance index are established by analysing the time evolution of the second order moment of the state and a recursive dynamic programming inequality respectively alternative conditions are derived for numerical implementations the proposed method is illustrated by numerical simulations

optimal output regulation for discrete time switched and markovian jump linear systems first three different but related output regulation performance criteria for the linear time varying system are defined in the discrete time domain namely the peak impulse response peak output variance and average output variance per unit time then they are extended for switched linear systems and markovian jump linear systems and characterized by an increasing union of finite dimensional linear matrix inequality conditions finally the infinite horizon suboptimal lqg control problem which aims to maintain the average output variance below a given level subject to the uniform exponential stability of the closed loop system is solved for both switched linear systems and markovian jump linear systems the solution is given by a dynamic linear output feedback controller that not only perfectly observes the present mode but also recalls a finite number of past modes

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

the effect of spatial information characterization on 3d local feature descriptors designing local feature descriptors for 3d objects is a fundamental yet challenging task in 3d computer vision both geometry and spatial information descriptions are critical for a 3d local descriptor while most previous studies concentrate on the former one this paper investigates on how the characterization of spatial information would affect a 3d local descriptor in terms of descriptiveness robustness compactness and efficiency the evaluation process is deployed as follows first based on the analysis of representative spatial information characterization methods of existing local shape descriptors six typical characterization methods with different spatial dimensions and partition principles of spatial information are presented second three geometric attributes i e normal deviation local depth and shape index are respectively assigned to each point in the local surface for local geometry description creating a total of 18 different feature descriptors then a quantitative analysis of performance i e descriptiveness robustness compactness and efficiency for these descriptors is carried out on three benchmark datasets grounded on the experimental outcomes the traits merits and demerits of each spatial information encoding approach are eventually summarized this study reveals that different spatial information encoding approaches would bring significant effect on a local shape descriptor with respect to its discriminative power stability compactness and efficiency highlightsthe effect of spatial information encoding sie on 3d local descriptors is emphasized eighteen types of 3d local descriptors with different sie approaches are proposed quantitative evaluation of sie approaches is performed on three standard datasets the merits demerits and suitable applications of different sie ways are summarized instructive guidance is concluded for the design of a 3d local descriptor

rotational projection statistics for 3d local surface description and object recognition recognizing 3d objects in the presence of noise varying mesh resolution occlusion and clutter is a very challenging task this paper presents a novel method named rotational projection statistics rops it has three major modules local reference frame lrf definition rops feature description and 3d object recognition we propose a novel technique to define the lrf by calculating the scatter matrix of all points lying on the local surface rops feature descriptors are obtained by rotationally projecting the neighboring points of a feature point onto 2d planes and calculating a set of statistics including low order central moments and entropy of the distribution of these projected points using the proposed lrf and rops descriptor we present a hierarchical 3d object recognition algorithm the performance of the proposed lrf rops descriptor and object recognition algorithm was rigorously tested on a number of popular and publicly available datasets our proposed techniques exhibited superior performance compared to existing techniques we also showed that our method is robust with respect to noise and varying mesh resolution our rops based algorithm achieved recognition rates of 100 98 9 95 4 and 96 0 respectively when tested on the bologna uwa queen s and ca foscari venezia datasets

a simple iterative method for resonance calculation a recently developed procedure for solving the stationary schrodinger equation in matrix representation form is proved to be useful in calculating quasibound energy levels results for a simple quantum mechanical model with potential energy function v r 1 lambda r lambda 0 are shown to be very accurate

a unified treatment of schrodinger s equation for anharmonic and double well potentials the authors exploit some exact soluble model potentials vn alpha beta v a b lambda x6 in order to extrapolate as lambda to 0 reliable eigenvalues of the one dimensional schrodinger equations with either anharmonic or symmetric double well potentials of the form v a b 1 2ax2 bx2 b 0 their procedure which corresponds to low order rayleigh schrodinger perturbation theory is found to be competitive with both high order pade summation of conventional rspt and large scale variational calculations using harmonic oscillators basis functions

on the local structure of optimal trajectories in r 3 we analyze the structure of a control function u t corresponding to an optimal trajectory for the system dot q f q u g q in a three dimensional manifold near a point where some nondegeneracy conditions are satisfied the kind of optimality which is studied includes time optimality the control turns out to be the concatenation of some bang and some singular arcs studying the index of the second variation of the switching times the number of such arcs is bounded by four

a condition for the stability of switched nonlinear systems in this paper we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems we show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems i e the lie bracket of any pair of them is zero are sufficient for the global asymptotic stability of the switched system we also show that these conditions are sufficient for the existence of a common lyapunov function

optimal control of discrete time bilinear systems with applications to switched linear stochastic systems abstract this paper aims at characterizing the most destabilizing switching law for discrete time switched systems governed by a set of bounded linear operators the switched system is embedded in a special class of discrete time bilinear control systems this allows us to apply the variational approach to the bilinear control system associated with a mayer type optimal control problem and a second order necessary optimality condition is derived optimal equivalence between the bilinear system and the switched system is analyzed which shows that any optimal control law can be equivalently expressed as a switching law this specific switching law is most unstable for the switched system and thus can be used to determine stability under arbitrary switching based on the second order moment of the state the proposed approach is applied to analyze uniform mean square stability of discrete time switched linear stochastic systems numerical simulations are presented to verify the usefulness of the theoretic results

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

passivity and feedback passification of switched discrete time linear systems abstract this paper focuses on the passivity analysis and feedback passification for switched discrete time linear systems using multiple storage functions under a certain switching law controllers and switching laws are designed based on complete and partial state measurements respectively conditions for strict passivity of a switched discrete time system are obtained without the requirement of strict passivity of subsystems in the case of partial state measurements dynamic output feedback controllers for subsystems are designed and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed loop switched system finally a numerical example is provided to demonstrate the feasibility of the theoretical results

brief paper a second order maximum principle for discrete time bilinear control systems with applications to discrete time linear switched systems a powerful approach for analyzing the stability of continuous time switched systems is based on using optimal control theory to characterize the most unstable switching law this reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific most unstable switching law for discrete time switched systems the variational approach received considerably less attention this approach is based on using a first order necessary optimality condition in the form of a maximum principle mp and typically this is not enough to completely characterize the most unstable switching law in this paper we provide a simple and self contained derivation of a second order necessary optimality condition for discrete time bilinear control systems this provides new information that cannot be derived using the first order mp we demonstrate several applications of this second order mp to the stability analysis of discrete time linear switched systems

snapshots a novel local surface descriptor and matching algorithm for robust 3d surface alignment in this paper a novel local surface descriptor is proposed and applied to the problem of aligning partial views of a 3d object the descriptor is based on taking snapshots of the surface over each point using a virtual camera oriented perpendicularly to the surface this representation has the advantage of imposing minimal loss of information be robust to self occlusions and also be very efficient to compute then we describe an efficient search technique to deal with the rotation ambiguity of our representation and experimentally demonstrate the benefits of our approaches which are pronounced especially when we align views with small overlap

stability of positive linear switched systems on ordered banach spaces abstract we provide sufficient criteria for the stability of positive linear switched systems on ordered banach spaces the switched systems can be generated by finitely many bounded operators in infinite dimensional spaces with a general class of order inducing cones in the discrete time case we assume an appropriate interior point of the cone whereas in the continuous time case an appropriate interior point of the dual cone is sufficient for stability this is an extension of the concept of linear lyapunov functions for positive systems to the setting of infinite dimensional partially ordered spaces we illustrate our results with examples

point signatures a new representation for 3d object recognition few systems capable of recognizing complex objects with free form sculptured surfaces have been developed the apparent lack of success is mainly due to the lack of a competent modelling scheme for representing such complex objects in this paper a new form of point representation for describing 3d free form surfaces is proposed this representation which we call the point signature serves to describe the structural neighbourhood of a point in a more complete manner than just using the 3d coordinates of the point being invariant to rotation and translation the point signature can be used directly to hypothesize the correspondence to model points with similar signatures recognition is achieved by matching the signatures of data points representing the sensed surface to the signatures of data points representing the model surface the use of point signatures is not restricted to the recognition of a single object scene to a small library of models instead it can be extended naturally to the recognition of scenes containing multiple partially overlapping objects which may also be juxtaposed with each other against a large model library no preliminary phase of segmenting the scene into the component objects is required in searching for the appropriate candidate model recognition need not proceed in a linear order which can become prohibitive for a large model library for a given scene signatures are extracted at arbitrarily spaced seed points each of these signatures is used to vote for models that contain points having similar signatures inappropriate models with low votes can be rejected while the remaining candidate models are ordered according to the votes they received in this way efficient verification of the hypothesized candidates can proceed by testing the most likely model first experiments using real data obtained from a range finder have shown fast recognition from a library of fifteen models whose complexities vary from that of simple piecewise quadric shapes to complicated face masks results from the recognition of both single object and multiple object scenes are presented

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

barrier lyapunov functions for the output tracking control of constrained nonlinear switched systems abstract in this paper we investigate the output tracking control problem of constrained nonlinear switched systems in lower triangular form first when all the states are subjected to constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approach some finite limits to prevent the states from violating the constraints based on the simultaneous domination assumption we design a continuous feedback controller for the switched system which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed loop signals remain bounded provided that the initial states are feasible then we further consider the case of asymmetric time varying output constraints by constructing an appropriate blf finally the effectiveness of the proposed results is demonstrated with a numerical example

brief paper markov jump linear systems with switching transition rates mean square stability with dwell time the stability of a class of markov jump linear systems characterized by piecewise constant transition rates and system dynamics is investigated for these switching markov jump linear systems mean square stability is analyzed through the time evolution of the second order moment of the state the main result is a sufficient condition that guarantees mean square stability under constraints on the dwell time between switching instants an alternative condition based on kronecker calculus is worked out it is shown that both the stability criteria admit an lmi implementation

toldi an effective and robust approach for 3d local shape description abstract feature description for the 3d local shape in the presence of noise varying mesh resolutions clutter and occlusion is a quite challenging task in 3d computer vision this paper tackles the problem by proposing a new local reference frame lrf together with a novel triple orthogonal local depth images toldi representation forming the toldi method for local shape description compared with previous methods toldi manages to perform efficient distinctive and robust description for the 3d local surface simultaneously under various feature matching contexts the proposed lrf differs from many prior ones in its calculation of the z axis and x axis the z axis is calculated using the normal of the keypoint and the x axis is computed by aggregating the weighted projection vectors of the radius neighbors toldi feature descriptors are then obtained by concatenating three local depth images ldi captured from three orthogonal view planes in the lrf into feature vectors the performance of our toldi approach is rigorously evaluated on several public datasets which contain three major surface matching scenarios namely shape retrieval object recognition and 3d registration experimental results and comparisons with the state of the arts validate the effectiveness robustness high efficiency and overall superiority of our method our method is also applied to aligning 3d object and indoor scene point clouds obtained by different devices i e lidar and kinect the accurate outcomes further confirm the effectiveness of our method

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

studies on algebraic methods to solve linear eigenvalue problems generalised anharmonic oscillators a detailed presentation of the recently introduced integration free method with applications to determine the energy levels of the generalised quantum anharmonic oscillators are given numerical calculations are realised for the quartic and the sextic oscillators energy eigenvalues obtained for the ground state as well as for the first few excited states accurate to thirty digits are very impressive and demonstrate the efficiency of the method certain remarks about the selection of the basis functions and a convergence discussion on the presented simple approximation scheme are also included in this paper

a simple iterative solution of the schrodinger equation in matrix representation form a simple procedure for solving the schrodinger equation is presented it is based upon an iterative solution of the secular equation a large enough convergence rate is obtained by using a basis set of properly scaled functions the effect of the scaling parameter on the convergence rate is studied in order to improve the calculation the method is applied to simple though non trivial quantum mechanical models such as the quartic sextic and octic anharmonic oscillators a double well potential and the linear confining potential highly accurate eigenvalues for all values of the coupling parameter are obtained

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

a maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems we consider a continuous time bilinear control system bcs with metzler matrices each entry in the transition matrix of such a system is nonnegative making the positive orthant an invariant set of the dynamics motivated by the stability analysis of positive linear switched systems plsss we define a control as optimal if for a fixed final time it maximizes the spectral radius of the transition matrix our main result is a first order necessary condition for optimality in the form of a maximum principle mp the proof of this mp combines the standard needle variation with a basic result from the perron frobenius theory of nonnegative matrices we describe several applications of this mp to the stability analysis of plsss under arbitrary switching

brief paper a unified design for state and output feedback h control of nonlinear stochastic markovian jump systems with state and disturbance dependent noise for a class of continuous time nonlinear stochastic markovian jump systems with state and disturbance dependent noise both the state and output feedback h control problems are studied based on the solvability of a set of coupled hamilton jacobi inequalities hjis we give a unified design for both state and dynamic output feedback h control via a common function u r t i e u x r t is a state feedback h control while u email protected r t is the desired output feedback h control

complementary variational principles and variational iterative principles complementary variational principles for the solution of certain linear equations are developed it is shown that these may be used iteratively for the solution of nonlinear equations examples are presented with applications in particle theory electromagnetic theory communication theory and the thomas fermi statistical theory for atoms

variational principles and variational iterative principles for a class of problems abstract complementary variational principles are developed for linear equations in a function space and a variational iterative scheme based on these principles is introduced for non linear equations

controllability of switched bilinear systems the controllability of switched bilinear systems sblss is considered three kinds of controllabilities including weak controllability approximate controllability and global controllability are investigated one by one sets of easily verifiable sufficient conditions are obtained for each case which are applicable to a large class of switched bilinear systems

a fast and robust local descriptor for 3d point cloud registration this paper proposes a novel local feature descriptor called a local feature statistics histogram lfsh for efficient 3d point cloud registration an lfsh forms a comprehensive description of local shape geometries by encoding their statistical properties on local depth point density and angles between normals the sub features in the lfsh descriptor are low dimensional and quite efficient to compute in addition an optimized sample consensus osac algorithm is developed to iteratively estimate the optimum transformation from point correspondences osac can handle the challenging cases of matching highly self similar models based on the proposed lfsh and osac a coarse to fine algorithm can be formed for 3d point cloud registration experiments and comparisons with the state of the art descriptors demonstrate that lfsh is highly discriminative robust and significantly faster than other descriptors meanwhile the proposed coarse to fine registration algorithm is demonstrated to be robust to common nuisances including noise and varying point cloud resolutions and can achieve high accuracy on both model data and scene data

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

technical communique analysis and design of aimd congestion control algorithms in communication networks we present a model of a network of synchronised sources operating additive increase multiplicative decrease aimd congestion control algorithms we show i that networks of such devices in the presence of a drop tail bottleneck buffer may be modelled as a positive linear system ii that such networks possess a unique stationary point and iii that this stationary point is globally exponentially stable we use these results to establish conditions for the fair co existence of traffic in networks employing heterogeneous aimd algorithms and to design a new protocol for operation over high speed and long distance links

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

quadratic optimal control of switched linear stochastic systems this paper studies a quadratic optimal control problem for discrete time switched linear stochastic systems with nonautonomous subsystems perturbed by gaussian random noises the goal is to jointly design a deterministic switching sequence and a continuous feedback law to minimize the expectation of a finite horizon quadratic cost function both the value function and the optimal control strategy are characterized analytically a numerical relaxation framework is developed to efficiently compute a control strategy with a guaranteed performance upper bound it is also proved that by choosing the relaxation parameter sufficiently small the performance of the resulting control strategy can be made arbitrarily close to the optimal one

instability of stochastic switched systems abstract the instability problem of stochastic switched systems is investigated in this paper definitions of instability are given in the forms of instability in probability m th instability moment exponential instability and almost sure exponential instability by the aid of dynkin s formula ito s formula and strong law of large numbers the criteria on instability of stochastic switched systems under arbitrary switching are established based on lyapunov like techniques simulation examples are presented to illustrate the validity of the results

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

a new approach to the eigenvalue problem in quantum mechanics convergent perturbation theory for rising potentials a new iteration procedure for solution of the schrodinger equation with arbitrary local potentials is proposed both the eigenvalues and eigenfunctions are represented in the form of a series which is well convergent under certain conditions the solution of the k dimensional schrodinger equation within the proposed scheme reduces to a problem of the k dimensional electrostatics as an example potentials x2n n 2 3 4 and m2x2 gx4 in one dimensional space are considered

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

correspondence comments on optimally switched linear systems the technical note titled optimally switched linear systems by the authors t das and r mukherjee addresses the problem of optimal switching for switched systems the proof of the theorem in the paper is incorrect and point out an important theoretical point which explains why the optimal switched solution does not exist whenever there exists a singular one to a relaxed problem this point has also important consequences concerning numerical difficulties encountered in solving such problems and are also discussed