nonlinear stability analysis for a class of differential integral systems arising from nuclear reactor dynamics a nonlinear stability analysis has been performed for mixed differential integral equations particularly applicable to nuclear reactors new general theorems of stability in bounded domains of initial perturbations have been introduced for a class of reactor models with an arbitrary reactivity feedback also effective stability criteria have been established for reactors with linear reactivity feedbacks for many kinds of models of phenomena typically encountered in nuclear reactors these new criteria give sharper stability bounds than criteria previously published the theoretical results obtained have been illustrated with examples of selected reactor models

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

stability of discrete bilinear systems with time delayed feedback functions the stability of discrete time varying bilinear systems is studied the control u t in the bilinear systems is considered as output feedback functions with time delay i e u t f y t y t 1 y t r 1 which is an important case and is absent in the literature also the authors assumed that the feedback function f is of larger classes than the classes given by current literature the sufficient conditions derived in theorems in the paper depend only on the coefficient matrices of the bilinear systems so that these results are convenient to check and to apply in engineering problems

exponential stability of general tracking algorithms tracking and adaptation algorithms are from a formal point of view nonlinear systems which depend on stochastic variables in a fairly complicated way the analysis of such algorithms is thus quite complicated a first step is to establish the exponential stability of these systems this is of interest in its own right and a prerequisite for the practical use of the algorithm it is also a necessary starting point to analyze the performance in terms of tracking and adaptation because that is how close the estimated parameters are to the time varying true ones in this paper we establish some general conditions for the exponential stability of a wide and common class of tracking algorithms this includes least mean squares recursive least squares and kalman filter based adaptation algorithms we show how stability of an averaged linear and deterministic equation and stability of the actual algorithm are linked to each other under weak conditions on the involved stochastic processes we also give explicit conditions for exponential stability of the most common algorithms the tracking performance of the algorithms is studied in a companion paper

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

on a stability theorem for nonlinear systems with slowly varying inputs recently m kelemen ieee trans automat contr vol ac 31 766 768 aug 1986 presented a stability result that deals with the response of a nonlinear system to slowly varying input signals in this work a proof is given under a weaker hypothesis on the input signal by constructing a lyapunov function that is standard in the control literature this proof may be more accessible than the other approaches for completeness brief proofs of some intermediate results that are regarded as well known are included a simple example is given to show that this approach can yield explicit bounds in certain situations of interest

diffusion tensor analysis with invariant gradients and rotation tangents guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation tensor shape and orientation both have three degrees of freedom spanned by invariant gradients and rotation tangents respectively as an initial demonstration of the framework we create a tunable measure of tensor difference that can selectively respond to shape and orientation second to analyze the spatial gradient in a tensor volume a third order tensor our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented finally we apply the framework to decompose the fourth order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance including a direct approximation for the variance of tensor invariants such as fractional anisotropy

multiresolution feature extraction and selection for texture segmentation an approach is described for unsupervised segmentation of textured images local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination local statistics texture energy measures are estimated at the output of an equivalent filter bank by means of a nonlinear transformation absolute value followed by an iterative gaussian smoothing algorithm this procedure generates a multiresolution sequence of feature planes with a half octave scale progression a feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions this approach provides a good approximation of r a fisher s 1950 multiple linear discriminants and has the advantage of requiring no a priori knowledge this feature reduction methods appears to be an improvement on the commonly used karhunen loeve transform and allows efficient texture segmentation based on simple thresholding

adaptive suboptimal filtering of bilinear systems the optimal filter minimum mean square error of discrete bilinear stochastic systems with output feedback is studied here the sequential filter of bilinear systems is derived for suboptimal adaptive estimation of the unknown a priori state and observation noise statistics simultaneously with the bilinear system state the unbiased estimations of state noise variance q and observation noise variance r are obtained under some usual conditions for on line operation this paper gives the recursive form of this adaptive suboptimal filter asf computer simulations show that asf approximates the minimum mean square error mse filter very well and asf provides improved state estimates at little computing expense

stability of discrete time bilinear systems with constant inputs in this paper discrete time bilinear systems are considered necessary and sufficient conditions are developed which ensure that for any constant input in an unbounded control domain the trajectories of the system tend to the origin as time increases

distributed averaging with random network graphs and noises we consider a discrete time distributed averaging algorithm over multi agent networks with measurement noises and time varying random graphs each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises the network structure is modeled by a sequence of time varying random digraphs which may be spatially and temporally dependent by stochastic lyapunov method and the combination of algebraic graph theory and martingale convergence theory we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus we prove that all states of the agents converge to a common random variable whose mathematical expectation is the average of initial values in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected an upper bound of the variance of the limit random variable that is the mean square steady state error for stochastic average consensus is given quantitatively related to the weights the algorithm gain and the energy level of the noises

support and approximation properties of hermite splines abstract in this paper we formally investigate two mathematical aspects of hermite splines that are relevant to practical applications we first demonstrate that hermite splines are maximally localized in the sense that the size of their support is minimal among pairs of functions with identical reproduction properties then we precisely quantify the approximation power of hermite splines for the reconstruction of functions and their derivatives it is known that the hermite and b spline approximation schemes have the same approximation order more precisely their approximation error vanishes as o t 4 when the step size t goes to zero in this work we show that they actually have the same asymptotic approximation error constants too therefore they have identical asymptotic approximation properties hermite splines combine optimal localization and excellent approximation power while retaining interpolation properties and closed form expression in contrast to existing similar functions these findings shed a new light on the convenience of hermite splines in the context of computer graphics and geometrical design

two dimensional spline interpolation for image reconstruction a scheme of two dimensional 2 d spline interpolation for image reconstruction is presented it is aimed to be applied in image data compression an impulse response derived from 2 d quadratic spline functions is theoretically analysed then it is approximated to be a finite duration one fir for practical implementation with this scheme compression rate of greater than 12 is achieved for x ray left ventricular cineangiogram image data compression

estimating intensity variance due to noise in registered images applications to diffusion tensor mri image registration techniques which require image interpolation are widely used in neuroimaging research we show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space we describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images the spatial transformations computed by the registration procedure and the interpolation or approximation kernel chosen the method is general and could handle various sources of signal variability such as thermal noise and physiological noise provided that their effects can be assessed in the original images our approach is applied to diffusion tensor dt mri data assuming only thermal noise as the source of variability in the data we show that incorrect noise variance estimates in registered diffusion weighted images can affect dt parameters as well as indices of goodness of fit such as chi square maps in addition to dt mri we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data such as in relaxometry and functional mri studies

least squares image resizing using finite differences we present an optimal spline based algorithm for the enlargement or reduction of digital images with arbitrary noninteger scaling factors this projection based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are b splines of any degree n a noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a for a given choice of basis functions the results of our method are consistently better than those of the standard interpolation procedure the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal to noise ratio the method can be generalized to include other classes of piecewise polynomial functions expressed as linear combinations of b splines and their derivatives

a stability property in this note we obtain a stability property not for a point of equilibrium but for a certain family of asymptotically stable equilibria of a dynamical system with an input we show that this property depends not only on the initial condition but also on the time derivative of the input function we suggest possible applications of this result to some control problems

stabilisation of discrete time bilinear systems by constant control inputs abstractin this paper the stabilisation problem of discrete time bilinear systems by using constant control inputs is considered it is shown that the spectrum of a matrix derived from the system

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

fast migration inversion with multivalued ray fields part 1 method validation test and application in 2d to marmousi we address the problem of building an efficient algorithm for ray based migration inversion in complex media characterized by multivalued traveltime since the multivalued ray maps can be computed by wavefront construction the key point lies in the interpolation of these multivalued coarse maps for this goal we propose two new strategies the first one is based on an interpolation of the rayfield after identifying the ray branches on the elementary cells of the coarse grid the second is based on an extrapolation of the arrivals from the coarse grid points both strategies are evaluated in two dimensions with the marmousi data set demonstrating the cpu efficiency and accuracy of both approaches since they both consider multiarrivals locally the associated overhead cost with respect to a single arrival implementation is quite low twice the computing time of the marmousi test case the application also reveals that the new interpolation strategy is more efficient in terms of cpu time compared to the extrapolation strategy but at the expense of a more complex numerical implementation and less accurate results

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

soft computing approach to feature extraction based on both wavelet theory and fuzzy theory a soft computing system scs is proposed for feature extraction of signals the proposed scs approach possesses the advantages of soft decision making on wavelet coefficients for feature extraction adaptive selectivity of mapping factors to coarse to fine resolution and compact form of feature representation with the scs feature extractor fuzzy sets are used to provide a robust representation for signal information and wavelet transform is used to decompose a signal into detail and approximation signals at a given resolution the detail and approximation signals are inputted to the proposed scs to extract signal features at that resolution level the sensitivity in feature extraction of the proposed approach can be adapted by tuning the fuzzy sets for the detail and approximation signals at different resolutions the signal can be examined and suitable features can be extracted examples of both one dimensional signals and two dimensional fingerprint images are used to illustrate the proposed soft computing approach for feature extraction and pattern recognition the results show that the extracted features are sensitive enough to distinguish the similar signal from the different ones and are robust enough to tolerate noise corruption

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

robust stability of state space models with structured uncertainties a method for robust eigenvalue location analysis of linear state space models affected by structured real parametric perturbations is proposed the approach based on algebraic matrix properties deals with state space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters a method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed the method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space this problem which can be reduced to finding the real solutions of a system of polynomial equations simplifies considerably when cases with one or two uncertain parameters are considered for these cases necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems

robust stabilization of uncertain systems in this paper we consider the systems described by dx axdt budt sum i sigma i f i xd beta i qquad text or qquad dot x ax bu sum i b i f i x t c i x and we will derive conditions under which there exists a feedback control law u kx such that the closed loop system is stable for all sigma i or smooth nonlinearities f i the nonlinearities f i and the noisy gains sigma i d beta i are unknown uncertainties in the system and the problem considered is to obtain a control law which is robust against these uncertainties as far as stability is concerned

simplified 2 d cubic spline interpolation scheme using direct computation algorithm it has been shown that the 2 d cubic spline interpolation csi proposed by truong is one of the best algorithms for image resampling or compression such a csi algorithm together with the image coding standard e g jpeg can be used to obtain a modified image codec while still maintaining a good quality of the reconstructed image for higher compression ratios in this paper a fast direct computation algorithm is developed to improve the computational efficiency of the original fft based 2 d csi methods in fact this algorithm computes the 2 d csi directly without explicitly calculating the complex division usually needed in the fft or winograd discrete fourier transform wdft algorithm in addition this paper describes a novel way to derivate the 2 d csi from the 1 d csi by using the row column method this new fast 2 d csi provides a regular and simple structure based upon linear correlations therefore it can be implemented by the use of a modification of kung s pipeline structure and is naturally suitable for vlsi implementations experimental results show that the proposed new fast 2 d csi algorithm can achieve almost the same csi performance with much fewer arithmetic operations in comparison with existing efficient algorithms

on approximations and ergodicity classes in random chains we study the limiting behavior of a random dynamic system driven by a stochastic chain our interest is in the chains that are not necessarily ergodic but are decomposable into ergodic classes to investigate the conditions under which the ergodic classes of a model can be identified we introduce and study an l1 approximation and infinite flow graph of the model we show that the l1 approximations of random chains preserve certain limiting behavior using the l1 approximations we show how the connectivity of the infinite flow graph is related to the structure of the ergodic groups of the model our main result of this paper provides conditions under which the ergodicity groups of the model can be identified by considering the connected components in the infinite flow graph we provide two applications of our main result to random networks namely broadcast over time varying networks and networks with random link failure

stabilization of a class of singularly perturbed bilinear systems the lyapunoy stability of a form of singularly perturbed bilinear system is investigated a theorem is proposed to show how to calculate the stabilizing controller for the whole system from a knowledge of the stability of the reduced order model a numerical example is given

brief paper target containment control of multi agent systems with random switching interconnection topologies in this paper the distributed containment control is considered for a second order multi agent system guided by multiple leaders with random switching topologies the multi leader control problem is investigated via a combination of convex analysis and stochastic process the interaction topology between agents is described by a continuous time irreducible markov chain a necessary and sufficient condition is obtained to make all the mobile agents almost surely asymptotically converge to the static convex leader set moreover conditions on the tracking estimation are provided for the convex target set determined by moving multiple leaders

stabilization of singularly perturbed strictly bilinear systems the stabilization problem via state feedback for the class of strictly bilinear singularly perturbed systems is considered it is shown that the stabilizing controller of the overall system can be determined by simply using the quadratic stabilizing controllers of the fast and slow subsystems the procedure for computing the two matrix gains of the controller is given and some illustrative examples are worked out

stability of discrete deterministic and stochastic nonlinear systems abstract in this paper we derive some sufficient conditions for local asymptotic stability and instability for discrete nonlinear deterministic and stochastic systems these theorems are easy to apply to specific discrete nonlinear systems some applications of our theorems to bilinear systems illustrate the above

synchronization in complex networks with stochastically switching coupling structures synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed a novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed some sufficient condition for a network with general time varying coupling structure to reach complete synchronization is provided based on the general theorem networks with stochastically switching coupling structures is investigated in particular two kinds of stochastic switching coupling networks are addressed a independent and identically distributed switching processes and b markov jump processes in both cases some sufficient condition for almost sure synchronization of the networks is given also numerical simulations are provided to illustrate the theoretical results

an efficient method for fitting large data sets using t splines data fitting is a fundamental tool in scientific research and engineering applications generally there are two ingredients in solving data fitting problems one is the fitting representation and the other is the fitting method nowadays the fitting of larger and larger quantities of data sets requires more compact fitting representation and faster fitting methods the t spline is a recently invented spline representation whose control mesh t mesh allows a row of control points to terminate thus reducing the number of superfluous control points in the b spline representation significantly this property makes t splines more compact than b splines in fitting large data sets however the adaptivity of the t spline causes the coefficient matrix of a least squares fitting linear system to lose its block structure thus when fitting large data sets with t splines by iterative methods only point iterative methods can be used and the iteration speeds of typically employed point iterative methods are r

self similarity part i splines and operators the central theme of this pair of papers parts i and ii in this issue is self similarity which is used as a bridge for connecting splines and fractals the first part of the investigation is deterministic and the context is that of l splines these are defined in the following terms s t is a cardinal l spline iff l s t sigma kisinza k delta t k where l is a suitable pseudodifferential operator our starting point for the construction of self similar splines is the identification of the class of differential operators l that are both translation and scale invariant this results into a two parameter family of generalized fractional derivatives parttau gamma where gamma is the order of the derivative and tau is an additional phase factor we specify the corresponding l splines which yield an extended class of fractional splines the operator parttau gamma is used to define a scale invariant energy measure the squared l2 norm of the gammath derivative of the signal which provides a regularization functional for interpolating or fitting the noisy samples of a signal we prove that the corresponding variational or smoothing spline estimator is a cardinal fractional spline of order 2gamma which admits a stable representation in a b spline basis we characterize the equivalent frequency response of the estimator and show that it closely matches that of a classical butterworth filter of order 2gamma we also establish a formal link between the regularization parameter lambda and the cutoff frequency of the smoothing spline filter omega0aplambda 2gamma finally we present an efficient computational solution to the fractional smoothing spline problem it uses the fast fourier transform and takes advantage of the multiresolution properties of the underlying basis functions

polynomial spline approximation of clarke s model we investigate polynomial spline approximation of stationary random processes on a uniform grid applied to clarke s model of time variations of path amplitudes in multipath fading channels with doppler scattering the integral mean square error mse for optimal and interpolation splines is presented as a series of spectral moments the optimal splines outperform the interpolation splines however as the sampling factor increases the optimal and interpolation splines of even order tend to provide the same accuracy to build such splines the process to be approximated needs to be known for all time which is impractical local splines on the other hand may be used where the process is known only over a finite interval we first consider local splines with quasioptimal spline coefficients then we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients in practice approximation with a low processing delay is of interest we investigate local spline extrapolation with a zero processing delay the results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error the error can be very close to the minimum error provided by optimal splines thus local splines can be effectively used for channel estimation in multipath fast fading channels

stability analysis of hybrid composite dynamical systems descriptions involving operators and differential equations we address the stability analysis of composite hybrid dynamical feedback systems of the type depicted in fig 1 consisting of a block usually the plant which is described by an operator l and of a finite dimensional block described by a system of ordinary differential equations usually the controller we establish results for the well posedness attractivity asymptotic stability uniform boundedness asymptotic stability in the large and exponential stability in the large for such systems the hypotheses of these results are phrased in terms of the i o properties of l and in terms of the lyapunov stability properties of the subsystem described by the indicated ordinary differential equations the applicability of our results is demonstrated by means of general specific examples involving c 0 semigroups partial differential equations or integral equations which determine l

comments on stabilization of a class of singularly perturbed bilinear systems asamoah and jamshidi 1987 investigated a stabilizing controller for singularly perturbed bilinear systems we point out that their result is incorrect unless another assumption is employed

addendum b spline interpolation in medical image processing analyzes b spline interpolation techniques of degree 2 4 and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging lehmann et al 1999 it is shown that high degree b spline interpolation has superior fourier properties smallest interpolation error and reasonable computing times therefore high degree b splines are preferable interpolators for numerous applications in medical image processing particularly if high precision is required if no aliasing occurs this result neither depends on the geometric transform applied for the tests nor the actual content of images

novel approaches to the parametric cubic spline interpolation the cubic spline interpolation csi scheme can be utilized to obtain a better quality reconstructed image it is based on the least squares method with cubic convolution interpolation cci function within the parametric csi scheme it is difficult to determine the optimal parameter for various target images in this paper a novel method involving the concept of opportunity costs is proposed to identify the most suitable parameter for the cci function needed in the csi scheme it is shown that such an optimal four point cci function in conjunction with the least squares method can achieve a better performance with the same arithmetic operations in comparison with the existing csi algorithm in addition experimental results show that the optimal six point csi scheme together with cross zonal filter is superior in performance to the optimal four point csi scheme without increasing the computational complexity

stabilization analysis of discrete nonlinear systems in this paper we set a new framework for the analysis of nonlinear discrete systems to carry out the stabilization theorem and to design stable controllers of the systems within that framework this framework includes many practically important systems described for example by lipschitz functions functions with arbitrary order bounded derivatives bilinear functions and all polynomial functions an important existence theorem for stabilizing has been proven for this framework the theorem basically states that under definite rather broad conditions the zero solution of the plants can be made stable by a nonlinear output feedback in addition this nonlinear feedback is from a larger class of functions than these classes given by current literature following these stabilization theorems a new design procedure for the output feedback control law is presented all results presented are easy to use and convenient to apply the application is illustrated by several examples including the design of stabilizing control for a bilinear control system

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

stability bounds of singularly perturbed discrete systems the authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems by combining three conditions of the critical stability criterion with a bialternate product for discrete time systems the stability problems of two types of singularly perturbed discrete time systems can be solved via the derived scheme several examples are given to illustrate the proposed results

the output stabilization of siso bilinear systems a quite general approach to the problem of stabilizing a siso single input single output bilinear system by output feedback is presented following a lyapunov like method a family of admissible controls is defined and an easy way for deriving its general features is proposed previous results can be obtained as special cases of this approach numerical examples are included to show the feasibility of this algorithm in determining simple control laws

stability analysis of bilinear systems the stability of the differential bilinear systems is studied the authors consider time varying bilinear systems with output feedback the input or control u t is not only a signal but also an input with output feedback i e u t f y t it is assumed that the feedback function f is in a function space which contains the class of linear functions functions satisfying the lipschitz condition and quadratic functions

robust stabilization of a class of singularly perturbed discrete bilinear systems this paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems the first one is an spl epsi dependent controller that stabilizes the closed loop system for all spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0 is the prespecified upper bound of the singular perturbation parameter the second one is an spl epsi independent controller which is able to stabilize the system in the entire state space for all spl epsi spl isin 0 spl epsi where spl epsi is the exact upper spl epsi bound the spl epsi can be calculated by the critical stability criterion once the robust controller is determined an example is presented to illustrate the proposed schemes

t s fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems this paper proposes a fuzzy bilinear model for a class of nonlinear systems and a fuzzy controller to stabilize such systems by examination of a modeling problem we describe how to transform a nonlinear system into a bilinear one via taylor s series expansion and then we adopt the takagi sugeno t s fuzzy modeling technique to construct a fuzzy bilinear model for controller design the parallel distributed compensation pdc method is utilized to stabilize the fuzzy bilinear system fbs and some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities lmis moreover we propound some sufficient conditions for robust stabilization of the fbs with parametric uncertainties finally a numerical example and the van de vusse model are utilized to demonstrate the validity and effectiveness of the proposed fbs

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

robustness of feedback stabilized systems in the presence of non linear and random perturbations the general robustness problem is discussed for a controlled discrete time system subject to a lur e type feedback non linearity together with random multiplicative noises effective on state input and the non linearity a sufficient condition is given utilizing the discrete stochastic version of the second method of lyapunov to guarantee that any stabilizing controller designed for the deterministic linear part of the system renders the closed loop system with perturbations asymptotically stable with probability one then specializations to systems given in controllability and controller canonical forms are made independent noise signals are assumed to be effective on individual parameters of these canonical forms whose inputs are designed to assign the closed loop poles to zero in these cases stronger results are obtained in terms of system parameters and known characteristics of perturbations

stabilizability conditions by memory less feedback for linear systems with time delay abstract sufficient conditions for the stabilization by a memoryless feedback of the system with time delay are derived the main results are as follows 1 if we can place the maximal eigenvalue of some matrix sufficiently left in the left hand plane the system with time delay can be stabilized by a memoryless feedback 2 if a certain dynamical system defined by the original system is minimum phase then stabilization by a memoryless feedback is possible

fast computation of the difference of low pass transform this paper defines the difference of low pass dolp transform and describes a fast algorithm for its computation the dolp is a reversible transform which converts an image into a set of bandpass images a dolp transform is shown to require o n2 multiplies and produce o n log n samples from an n sample image when gaussian low pass filters are used the result is a set of images which have been convolved with difference of gaussian dog filters from an exponential set of sizes a fast computation technique based on resampling is described and shown to reduce the dolp transform complexity to o n log n multiplies and o n storage locations a second technique cascaded convolution with expansion is then defined and also shown to reduce the computational cost to o n log n multiplies combining these two techniques yields an algorithm for a dolp transform that requires o n storage cells and requires o n multiplies

a continuous time linear system identification method for slowly sampled data both direct and indirect methods exist for identifying continuous time linear systems a direct method estimates continuous time input and output signals from their samples and then use them to obtain a continuous time model whereas an indirect method estimates a discrete time model first both methods rely on fast sampling to ensure good accuracy in this paper we propose a more direct method where a continuous time linear model is directly fitted to the available samples this method produces an exact model asymptotically modulo some possible aliasing ambiguity even when the sampling rate is relatively slow we also state conditions under which the aliasing ambiguity can be resolved and we provide experiments showing that the proposed method is a valid option when a slow sampling frequency must be used but a large number of samples is available

multiresolution approximation using shifted splines we consider the construction of least squares pyramids using shifted polynomial spline basis functions we derive the pre and post filters as a function of the degree n and the shift parameter spl delta we show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples respectively we introduce a measure of shift invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points i e spl delta 1 2 when n is odd and spl delta 0 when n is even the worst case corresponds to the standard multiresolution setting where the spline spaces are nested

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

computation of wavelet coefficients from average samples there exist efficient methods to compute the wavelet coefficients of a function f t from its point samples f t email protected email protected n however in many applications the available samples are average samples of the type f t email protected u t dt where the averaging function u t reflects the characteristic of the acquisition device in this work methods to compute the coefficients in a biorthogonal wavelet system from average samples are studied error estimations are obtained and using them the optimal values for the parameters in the proposed approximation rules are calculated the obtained error estimations can also be applied to the rules that compute the coefficients from point samples and thus these estimations can be used to compare and to choose between the different methods proposed in the literature the methods proposed here also allow us to compute the biorthogonal wavelet coefficients from the coefficients in another biorthogonal wavelet system

cluster consensus in discrete time networks of multiagents with inter cluster nonidentical inputs in this paper cluster consensus of multiagent systems is studied via inter cluster nonidentical inputs here we consider general graph topologies which might be time varying the cluster consensus is defined by two aspects intracluster synchronization the state at which differences between each pair of agents in the same cluster converge to zero and inter cluster separation the state at which agents in different clusters are separated for intra cluster synchronization the concepts and theories of consensus including the spanning trees scramblingness infinite stochastic matrix product and hajnal inequality are extended as a result it is proved that if the graph has cluster spanning trees and all vertices self linked then the static linear system can realize intra cluster synchronization for the time varying coupling cases it is proved that if there exists t 0 such that the union graph across any t length time interval has cluster spanning trees and all graphs has all vertices self linked then the time varying linear system can also realize intra cluster synchronization under the assumption of common inter cluster influence a sort of inter cluster nonidentical inputs are utilized to realize inter cluster separation such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs in addition the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory as an application we employ a modified non bayesian social learning model to illustrate the effectiveness of our results

fractional splines and wavelets we extend schoenberg s family of polynomial splines with uniform knots to all fractional degrees alpha 1 these splines which involve linear combinations of the one sided power functions x alpha max 0 x alpha are alpha holder continuous for alpha 0 we construct the corresponding b splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains we show that these functions satisfy most of the properties of the traditional b splines including the convolution property and a generalized fractional differentiation rule that involves finite differences only we characterize the decay of the b splines that are not compactly supported for nonintegral alpha s their most astonishing feature in reference to the strang fix theory is that they have a fractional order of approximation alpha 1 while they reproduce the polynomials of degree lceil alpha rceil for alpha frac 1 2 they satisfy all the requirements for a multiresolution analysis of ll 2 riesz bounds two scale relation and may therefore be used to build new families of wavelet bases with a continuously varying order parameter our construction also yields symmetrized fractional b splines which provide the connection with duchon s general theory of radial m s splines including thin plate splines in particular we show that the symmetric version of our splines can be obtained as the solution of a variational problem involving the norm of a fractional derivative

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

composite fuzzy control of nonlinear singularly perturbed systems this paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed nsp systems with guaranteed hinfin control performance we use the takagi sugeno t s fuzzy model to construct the singularly perturbed fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained at first a set of common positive define matrices and the controller gains are determined by the lyapunov stability theorem and linear matrix inequality lmi approach then a sufficient condition is derived for the robust stabilization of nsp systems the composite fuzzy control will stabilize the original nsp systems for all epsivisin 0 epsiv and the allowable perturbation bound epsiv can be determined via some algebra inequalities a practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme

quasi interpolation by means of filter banks we consider the problem of approximating a regular function f t from its samples f nt taken in a uniform grid quasi interpolation schemes approximate f t with a dilated version of a linear combination of shifted versions of a kernel t specifically fapprox t t af n t t n in a way that the polynomials of degree at most l 1 are recovered exactly these approximation schemes give order l i e the error is o tl where t is the sampling period recently quasi interpolation schemes using a discrete prefiltering of the samples f nt to obtain the coefficients af n have been proposed they provide tight approximation with a low computational cost in this work we generalize considering rational filter banks to prefilter the samples instead of a simple filter this generalization provides a greater flexibility in the design of the approximation scheme the upsampling and downsampling ratio r of the rational filter bank plays a significant role when r 1 the scheme has similar characteristics to those related to a simple filter approximation schemes corresponding to smaller ratios give less approximation quality but in return they have less computational cost and involve less storage load in the system

polynomial spline signal approximations filter design and asymptotic equivalence with shannon s sampling theorem the least squares polynomial spline approximation of a signal g t in l sub 2 r is obtained by projecting g t on s sup n r the space of polynomial splines of order n it is shown that this process can be linked to the classical problem of cardinal spline interpolation by first convolving g t with a b spline of order n more specifically the coefficients of the b spline interpolation of order 2n 1 of the sampled filtered sequence are identical to the coefficients of the least squares approximation of g t of order n it is shown that this approximation can be obtained from a succession of three basic operations prefiltering sampling and postfiltering which confirms the parallel with the classical sampling reconstruction procedure for bandlimited signals the frequency responses of these filters are determined for three equivalent spline representations using alternative sets of shift invariant basis functions of s sup n r the standard expansion in terms of b spline coefficients a representation in terms of sampled signal values and a representation using orthogonal basis functions

image data compression using cubic convolution spline interpolation a new cubic convolution spline interpolation ccsi for both one dimensional 1 d and two dimensional 2 d signals is developed in order to subsample signal and image compression data the ccsi yields a very accurate algorithm for smoothing it is also shown that this new and fast smoothing filter for ccsi can be used with the jpeg standard to design an improved jpeg encoder decoder for a high compression ratio

biorthogonal partners and applications two digital filters h z and f z are said to be biorthogonal partners of each other if their cascade h z f z satisfies the nyquist or zero crossing property biorthogonal partners arise in many different contexts such as filterbank theory exact and least squares digital interpolation and multiresolution theory they also play a central role in the theory of equalization especially fractionally spaced equalizers in digital communications we first develop several theoretical properties of biorthogonal partners we also develop conditions for the existence of biorthogonal partners and fir biorthogonal pairs and establish the connections to the riesz basis property we then explain how these results play a role in many of the above mentioned applications

convergence rate for discrete time multiagent systems with time varying delays and general coupling coefficients multiagent systems mass are ubiquitous in our real world there is an increasing attention focusing on the consensus or synchronization problem of mass over the past decade although there are numerous results reported on the convergence of a discrete time mas based on the infinite products of matrices few results are on the convergence rate because of the switching topology the traditional eigenvalue analysis and the lyapunov function methods are both invalid for the convergence rate analysis of an mas with a switching topology therefore the estimation of the convergence rate for a discrete time mas with time varying delays remains a difficult problem to overcome the essential difficulty of switching topology this paper aims at developing a contractive set approach to analyze the convergence rate of a discrete time mas in the presence of time varying delays and generalized coupling coefficients using the proposed approach we obtain an upper bound of the convergence rate under the condition of joint connectivity in particular the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients which have been widely applied in the existing works on this topic as an application of the main results we will show that the classical vicsek model with time delays can realize synchronization if the initial topology is connected

consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes in this paper we discuss the consensus problem in networks of multiagents with stochastically switching topologies the switch of graph topology is modeled as an adapted stochastic process which in principle can include any stochastic processes such as independent and identically distributed i i d processes and markov chains we derive the sufficient conditions for consensus in both discrete time and continuous time networks in terms of conditional expectations of the underlying graph topology we prove that if there exist t 0 and delta 0 such that the conditional expectation of the union of the delta graph topologies across each t length time interval has spanning trees then the multiagent system reaches consensus for comparison we show that some previous results on this topic can be derived from our main theorem as corollaries this includes important results when the switching topology can be modeled as the special and important stochastic models the i i d process and the markov process which implies that we generalize the previous results to some extent as applications we also give some corollaries concerning stochastic processes other than the i i d process and markov processes such as independent but not necessarily identically distributed processes hidden markov models and phi mixing processes

a layered analysis of consensus this paper introduces a simple notion of layering as a tool for analyzing well behaved runs of a given model of distributed computation using layering a model independent analysis of the consensus problem is performed and then applied to proving lower bounds and impossibility results for consensus in a number of familiar and less familiar models the proofs are simpler and more direct than existing ones and they expose a unified structure to the difficulty of reaching consensus in particular the proofs for the classical synchronous and asynchronous models now follow the same outline a new notion of connectivity among states in runs of a consensus protocol called potence connectivity is introduced this notion is more general than previous notions of connectivity used for this purpose and plays a key role in the uniform analysis of consensus

a fast efficient computation of cubic spline interpolation in image codec it is shown that cubic spline interpolation csi can be performed by a fast and efficient computation for the encoding and decoding processes of image coding it requires substantially fewer additions and multiplications than the original csi algorithm furthermore a new type of overlap save scheme is utilized to solve the boundary condition problems that occur between two neighboring subimages in the actual image it is also shown that a very efficient nine point winograd discrete fourier transform wdft can be used to replace the fast fourier transform fft needed to implement the csi scheme in the modified jpeg encoder finally the proposed fast new csi algorithm with a compression ratio of 9 1 is used along with the jpeg standard to speed up the modified jpeg encoder decoder and still obtain a better quality of reconstructed image for higher compression ratios

stability of discrete bilinear systems with output feedback abstract time varying discrete bilinear systems with output feedback are considered sufficient conditions ensuring the stability and asymptotic stability of discrete bilinear systems with output feedback are derived these sufficient conditions depend only on the coefficient matrices of the bilinear systems thus they are convenient to check and easy to apply in engineering practice

consensus over ergodic stationary graph processes in this technical note we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process we prove that consensus algorithms converge almost surely if and only if the expected graph of the network contains a directed spanning tree our results contain the case of independent and identically distributed graph processes as a special case we also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate

interpolation artifacts in sub pixel image registration we consider the problem of registering aligning two images to sub pixel accuracy by optimization of objective functions constructed from the images intensity values we show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which if not counter balanced by other terms can cause local optima in registration objective functions including the sum of squared differences cross correlation and mutual information we discuss different solutions to address the problem based on high degree b spline interpolation low pass filtering the images and stochastic integration numerical examples using synthetic and real signals and images are shown

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

on asymptotically stabilizing feedback control of bilinear systems asymptotically stabilizing feedback controls for a class of bilinear systems are discussed a simple modification which strengthens a result of slemrod 1 is noted and illustrated by example