enhanced detectability of small objects in correlated clutter using an improved 2 d adaptive lattice algorithm two dimensional 2 d adaptive filtering is a technique that can be applied to many image processing applications this paper will focus on the development of an improved 2 d adaptive lattice algorithm 2 d al and its application to the removal of correlated clutter to enhance the detectability of small objects in images the two improvements proposed here are increased flexibility in the calculation of the reflection coefficients and a 2 d method to update the correlations used in the 2 d al algorithm the 2 d al algorithm is shown to predict correlated clutter in image data and the resulting filter is compared with an ideal wiener hopf filter the results of the clutter removal will be compared to previously published ones for a 2 d least mean square lms algorithm 2 d al is better able to predict spatially varying clutter than the 2 d lms algorithm since it converges faster to new image properties examples of these improvements are shown for a spatially varying 2 d sinusoid in white noise and simulated clouds the 2 d lms and 2 d al algorithms are also shown to enhance a mammogram image for the detection of small microcalcifications and stellate lesions

local stabilization of linear systems under amplitude and rate saturating actuators this note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation considering the actuator represented by a first order system subject to input and state saturation a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stability results from this condition an algorithm based on the iterative solution of linear matrix inequalities based problems is proposed in order to compute the control law

performance evaluation of 2 d adaptive prediction filters for detection of small objects in image data this work studies the performance of dimensional least mean square tdlms adaptive filters as prewhitening filters for the detection of small objects in image data the object of interest is assumed to have a very small spatial spread and is obscured by correlated clutter of much larger spatial extent the correlated clutter is predicted and subtracted from the input signal leaving components of the spatially small signal in the residual output the receiver operating characteristics of a detection system augmented by a tdlms prewhitening filter are plotted using monte carlo techniques it is shown that such a detector has better operating characteristics than a conventional matched filter in the presence of correlated clutter for very low signal to background ratios tdlms based detection systems show a considerable reduction in the number of false alarms the output energy in both the residual and prediction channels of such filters is shown to be dependent on the correlation length of the various components in the input signal false alarm reduction and detection gains obtained by using this detection scheme on thermal infrared sensor data with known object positions is presented

on the uniform exponential stability of a wide class of linear time delay systems this paper deals with the global uniform exponential stability independent of delay of time delay linear and time invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities it is assumed that the delay free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay respectively the auxiliary system is typically a part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature since there is a great freedom in setting such an auxiliary system the obtained stability conditions are very useful in a wide class of practical applications

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

adaptive stabilization of non necessarily inversely stable first order systems by using estimates modification based on testing the sylvester determinant this paper presents an adaptive control scheme for first order continuous time systems the estimated plant model is controllable and then the adaptive scheme is free from singularities the singularities are avoided through a modification of the a priori estimated plant parameter vector so that its associated sylvester matrix is guaranteed to be non singular that property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold in addition the use of a hysteresis switching function is not required for a modification of the estimates the global asymptotic stability of the closed loop scheme is ensured it is also proved that the problem is well posed even if chattering motion exists due to the modification process the results are also extended to the case of presence of uncertainties consisting of bounded noise and a class of unmodelled dynamics so that global stability of the scheme is ensured in this last case relative adaptation zones are used on the a priori estimates for robust stabilization purposes so that the estimation process is frozen when the size of the prediction error is small compared to the contribution of the unmodelled dynamics to the plant output

enhancement of sinusoids in colored noise and the whitening performance of exact least squares predictors the extraction of sinusoids in white noise using least squares predictors has attracted a lot of attention in the past mainly in the context of the adaptive line enhancer ale however very few results exist for the practical colored noise case or for the whitening performance of the predictors we use a matrix formulation to derive the optimal least squares coefficients and frequency response of the d step predictor or ale for sinusoids real or complex in additive colored noise several cases are considered and in particular new formulas for the amplitude gain are obtained in low pass background noise the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency and a decreasing function for high pass noise for the whitening application signal to noise ratio snr bounds of the output are derived when the input is a white signal plus a sinusoidal interference we also give a state space model and stochastic interpretations of our analysis of the d step predictor providing connections to other related areas to enable filtering of nonstationary complex inputs as well as multichannel and multiexperiment data a complex vector version of the ladder algorithm is presented that can be used to implement the ale noise cancelling and noise inversion for narrow band interference rejection

two dimensional block diagonal lms adaptive filtering the paper is concerned with the development of two dimensional 2d adaptive filters using the block diagonal least mean squared bdlms method in this adaptive filtering scheme the image is scanned and processed block by block in a diagonal fashion and the filter weights are adjusted once per block rather than once per pixel the diagonal scanning is adopted to avoid the problems inherent in the 1d standard scanning schemes and to account for the correlations in two directions the weight updating equation for 2d bdlms is derived and the convergence properties of the algorithms are investigated simulation results that indicate the effectiveness of the 2d bdlms when used for image enhancement estimation and detection applications are presented

fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms the objective of this research is to model the mammographic parenchymal and ductal patterns and enhance the microcalcifications using a deterministic fractal approach according to the theory of deterministic fractal geometry images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional 2 d affine transformations the iterated functions systems and the collage theorem are the mathematical foundations of fractal image modeling here a methodology based on fractal image modeling is developed to analyze and model breast background structures the authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations therefore microcalcifications can be enhanced by taking the difference between the original image and the modeled image the authors results are compared with those of the partial wavelet reconstruction and morphological operation approaches the results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications it may also be able to improve the detection and classification of microcalcifications in a computer aided diagnosis system

parameter dependent lyapunov functions for robust stability of time varying linear systems under point delays abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays the matrices describing the state space dynamics are parameterized by in general time varying function matrices governed by coefficient functions in compact sets the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing parameter dependent candidates which satisfy in the most general case a riccati matrix differential inequality

infrared patch image model for small target detection in a single image the robust detection of small targets is one of the key techniques in infrared search and tracking applications a novel small target detection method in a single infrared image is proposed in this paper initially the traditional infrared image model is generalized to a new infrared patch image model using local patch construction then because of the non local self correlation property of the infrared background image based on the new model small target detection is formulated as an optimization problem of recovering low rank and sparse matrices which is effectively solved using stable principle component pursuit finally a simple adaptive segmentation method is used to segment the target image and the segmentation result can be refined by post processing extensive synthetic and real data experiments show that under different clutter backgrounds the proposed method not only works more stably for different target sizes and signal to clutter ratio values but also has better detection performance compared with conventional baseline methods

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

fuzzy sliding mode controller design for uncertain time delayed systems with nonlinear input in this paper the theory of sliding mode control is employed to develop a fuzzy controller for uncertain dynamic time delayed systems with series nonlinearities the control method provides a simple way to achieve asymptotic stability of the uncertain time delayed system other attractive features of the method include a minimal realization of the fuzzy controller in spite of the number of state variables as well as insensitivity to the uncertainties and disturbances in addition the method is capable of handling the chattering problem inherent to the sliding mode control easily and effectively also this fuzzy sliding mode controller can be extended to handle the mimo system simulation results are presented to demonstrate the power of the method

new stability performance results for singularly perturbed systems the guardian map theory of generalized stability of parametrized linear time invariant systems is used to prove new results on stability performance of linear time invariant singularly perturbed systems with an exogenous parameter i e systems that contain in addition to a singular parameter another uncertain parameter the results give necessary and sufficient conditions for generalized stability for all sufficiently small values of and all values of in a given interval 1 2 in addition explicit expressions for the largest upper bound on for guaranteed stability and performance are given and the cases leading to finite or infinite are clearly delineated thus the results represent a significant addition to the classical klimushev krasovskii theorem while at the same time providing closed form expressions for the maximum parameter range for stability and performance

multiparameter singular perturbation problems iterative expansions and asymptotic stability abstract recursive formulae are derived which yield asymptotic expansions for the eigenvalues of multiparameter singular perturbation problems these formulae follow readily from an exact expression for the eigenvalues which involves an implicit matrix function the implicit function satisfies an algebraic matrix riccati equation reminiscent of a similar equation of the single parameter theory the results also explicate the block d stability criterion for asymptotic stability previously introduced by khalil and kokotovic

two dimensional linear prediction and its application to adaptive predictive coding of images this paper summarizes a study on two dimensional linear prediction of images and its application to adaptive predictive coding of monochrome images the study was focused on three major areas two dimensional linear prediction of images and its performance implementation of an adaptive predictor and adaptive quantizer for use in image coding and linear prediction and adaptive predictive coding of density logarithm of intensity images among the issues investigated are autoregressive modeling of 2 d image sequences estimation of the nonzero average bias of the image samples stability of the inverse prediction error filter and estimation of the parameters of a 2 d separable linear predictor the implementation of the adaptive predictor is based on the results of linear predictive analysis the adaptive quantization of the prediction error signal is done by using a flexible three level quantizer for code words of fixed or variable length the above ideas are further applied to density images for exploiting the multiplicative structure of images the results of this research indicate that by using adaptive prediction and quantization intensity and density coded images of high quality can be obtained at information rates as low as 0 7 bits pixel

robust hurwitz stability test for linear systems with uncertain commensurate time delays the note deals with the robust hurwitz stability of a class of linear systems with uncertain commensurate time delays which is formulated as the robust hurwitz stability of a nonpolytopic family of quasi polynomials a np hard problem from the viewpoint of computational complexity on the basis of the edge theorem and sylvester resultant elimination a necessary and sufficient condition is developed for the robust stability of the whole family and it yields an effective testing procedure an illustrative example is given to show the effectiveness of the method

stability criteria for linear time invariant systems with multiple delays two new asymptotic stability criteria for linear time invariant systems with multiple delays are established by using a quadratic inequality lemma together with frequency domain techniques one criterion is for delay dependent stability and another is for delay independent asymptotic stability each of them has only one tuning parameter matrix p 0 as the lyapunov type stability criteria for the corresponding linear time invariant systems without delays do both of the established stability criteria are given in the form of lmi problems and hence are very easy to use in applications in addition it is remarked that the established delay independent asymptotic stability criterion with one tuning parameter matrix p 0 improves and simplifies the existing criterion with more than one tuning parameter matrix in the literature

robust adaptive control of discrete nominally stabilizable plants this paper presents an indirect pole placement based adaptive control scheme for discrete linear time invariant non necessarily inversely stable and stabilizable systems the scheme is a pole placement type without requiring the plant inverse stability assumption the control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal given by an arbitrary stable filter under a bounded tracking error while ensuring robust closed loop stability the adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and possibly bounded disturbances are proved without assuming the controllability of the modeled plant a normalized least squares algorithm with a relative adaptation dead zone and a posteriori modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit such a property is crucial to solve the stable pole placement problem on the other hand the relative adaptation dead zone is included for robustness purposes under unmodeled dynamics and possibly bounded disturbances

stochastic model based processing for detection of small targets in non gaussian natural imagery stochastic background models incorporating spatial correlations can be used to enhance the detection of targets in natural terrain imagery but are generally difficult to apply when the statistics are non gaussian chapple and bertilone see opt commun vol 150 p 71 76 1998 proposed a simple stochastic model for images of natural backgrounds based on the pointwise nonlinear transformation of gaussian random fields and demonstrated its effectiveness and computational efficiency in modeling the textures found in natural terrain imagery acquired from airborne ir sensors in this paper we show how this model can be used to design algorithms that detect small targets up to several pixels in size in natural imagery by identifying anomalous regions of the image where the statistics differ significantly from the rest of the background all of the model based algorithms described here involve nonlinear spatial processing prior to the final decision threshold monte carlo testing reveals that the model based algorithms generally perform better than both the adaptive threshold filter and the generalized matched filter for detecting low contrast targets despite the fact that they do not require the target statistics needed for constructing the matched filter

a new parameter estimate in singular perturbations abstract a new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system general time invariant systems with a single small parameter are considered the paper employs a riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics an application of the brouwer fixed point theorem to the riccati equation and of liapunov s direct method to the fast and slow subsystems results in the desired upper bound computation of the estimate requires only the solution of two liapunov matrix equations

on the stability bounds of singularly perturbed systems the stability bound problem of linear time invariant singularly perturbed systems is considered a set of new stability conditions based on the frequency domain representation is derived the stability criteria can be easily verified by computing certain singular values within finite frequency intervals illustrative examples show that the proposed criteria actually induce a less conservative epsilon bound than the existing criteria and for certain cases an infinite epsilon bound may be obtained

technical communique on the klimushchev krasovskii theorem the klimushchev krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems motivated by some subtle examples this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the klimushchev krasovskii theorem this note also extends the main inertia theorem to singularly perturbed systems

adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays the problem of robust tracking and model following is considered for a class of linear systems with multiple delayed state perturbations time varying uncertain parameters and disturbance in this note it is assumed that the upper bounds of the delayed state perturbations uncertainties and external disturbances are unknown an improved adaptation law with spl sigma modification is proposed to estimate such unknown bounds and on the basis of the updated values of these unknown bounds a class of continuous memoryless state feedback controllers is constructed for robust tracking of dynamical signals the proposed adaptive robust tracking controller can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations time varying uncertain parameters and disturbance in addition it is also shown that this improved adaptation law with spl sigma modification can be applied to the general adaptive control problems to obtain some more exact control results finally a numerical example is given to demonstrate the validity of the results

two dimensional joint process lattice for adaptive restoration of images the two dimensional 2d joint process lattice tdjpl and its implementations for image restoration applications are examined a 2d adaptive lattice algorithm tdal is first developed convergence properties of the algorithm are covered for the 2d adaptive lattice least mean squares tdal lms case the complexity of the normalized algorithm is slightly more than that of the tdal lms but it is a faster converging algorithm implementations of the proposed tdjpl estimator as a 2d adaptive lattice noise canceler and as a 2d adaptive lattice line enhancer are then considered the performance of both schemes is evaluated using artificially degraded image data at different signal to noise ratios snrs the results show that substantial noise reduction has been achieved and the high improvement in the mean square error even at very low input snr is ensured the results obtained consistently demonstrate the efficacy of the proposed tdjpl implementations and illustrate the success in its use for adaptive restoration of images

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

singular perturbation of strictly positive realness abstract the robustness of the strictly positive real spr condition of linear time invariant multi input multi output lti mimo singularly perturbed systems is examined a necessary and sufficient condition under which the full system is spr is proved this robustness result is an extension of the analysis for the popov kalman yakubovich lemma by v r saksena and p v kokotovic 7

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

synthesis of controllers for continuous time delay systems with saturating controls via lmis the stabilization of linear continuous time systems with time delay in the state and subject to saturating controls is addressed sufficient conditions obtained via a linear matrix inequality lmi formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements the method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed loop system is guaranteed when control saturations effectively occur

stabilization of exponentially unstable linear systems with saturating actuators we study the problem of stabilizing exponentially unstable linear systems with saturating actuators the study begins with planar systems with both poles exponentially unstable for such a system we show that the boundary of the domain of attraction under a saturated stabilizing linear state feedback is the unique stable limit cycle of its time reversed system a saturated linear state feedback is designed that results in a closed loop system having a domain of attraction that is arbitrarily close to the null controllable region this design is then utilized to construct state feedback laws for higher order systems with two exponentially unstable poles

adaptive enhancement of finite bandwidth signals in white gaussian noise the steady state behavior of the adaptive line enhancer ale is analyzed for stationary inputs consisting of finite bandwidth signals embedded in a white gaussian noise wgn background analytic expressions for the weights and output of the lms adaptive filter are derived as functions of input signal bandwidth and snr as well as ale length and bulk delay the steady state gain in broad band snr from input to output is derived as a function of these same four variables for fixed ale parameters and input snr it is shown that this gain increases as the input signal becomes narrower and approaches the sinusoidal limit it is emphasized that because the correlation time of finite bandwidth signals is limited excessively large values of the ale bulk delay parameter result in diminished gain furthermore there is an optimal filter length whose value depends upon signal bandwidth and snr for which the broad band gain is maximized these results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real time adaptive processors

robust stability of time varying polytopic systems abstract this paper provides global asymptotic stability conditions for time varying continuous time polytopic systems using a parameter dependent lyapunov function the time varying parameter uncertainty as well as its time derivative are modelled as belonging to polytopic convex sets and their dependence is made explicit to get less conservative results a particular case characterized by the parameter uncertainty satisfying a linear differential equation is analyzed and a simpler version of the aforementioned stability conditions is presented the results are expressed in terms of linear matrix inequalities being thus numerically solvable with no big difficulty the theory is illustrated by the determination of the asymptotic stability region of a mathieu s type equation with an uncertain time varying parameter

robust stabilization of a class of polytopic linear time varying continuous systems under point delays and saturating controls abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays under saturating state feedback controls the matrices describing the state space dynamics and control belong to polytopes also the controller gain matrix is characterized as belonging to another polytope whose vertices are computed from the knowledge of a closed bounded ball containing a set of values of the state norm and also the component wise saturating gains and saturation parameterizations this knowledge defines the polytope vertices through scaling diagonal matrices being associated with the various operation modes in the linear and saturated zones of each input component in these conditions the resulting closed loop system is of polytopic nature whose whole number of vertices is at most equal to the product of both numbers of vertices of the above two polytopes characterizing the plant parameterization and the saturation the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing candidates for each vertex of the polytopic closed loop system each satisfying in the most general case a riccati matrix differential inequality some conditions guaranteeing the stability conditions are obtained from a general kalman yakubovitch popov kyp lemma and some weaker stability conditions are also obtained for the time invariant case from a set of linear matrix inequalities associated with the set of vertices

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods