adaptive pole positioning in mimo linear systems by periodic multirate input controllers abstract in this paper the certainty equivalence principle is used to combine the identification method with a control structure derived from the pole placement problem which rely on periodic multirate input controllers the proposed adaptive pole placers contain a sampling mechanism with different sampling period to each system input and rely on a periodically varying controller which suitably modulates the sampled outputs and reference signals of the plant under control such a control strategy allows us to arbitrarily assign the poles of the sampled closed loop system in desired locations and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system and the knowledge of a set of structural indices namely the locally minimum controllability indices of the continuous time plant an indirect adaptive control scheme is derived which estimates the unknown plant parameters and consequently the controller parameters on line from sequential data of the input and outputs of the plant which are recursively updated within the time limit imposed by a fundamental sampling period t0 using the proposed algorithm the controller determination is based on the transformation of the discrete analogous of the system under control to a phase variable canonical form prior to the application of the control design procedure the solution of the problem can then be obtained by a quite simple utilization of the concept of state similarity transformation known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial diophantine equation thus introducing high order exogenous dynamics in the control loop moreover in many cases the solution of the diophantine equation for a desired set of closed loop eigenvalues might yield an unstable controller and the overall adaptive pole placement scheme is unstable with unstable compensators because their outputs are unbounded the proposed control strategy avoids these problems since here gain controllers are essentially needed to be designed moreover persistency of excitation and therefore parameter convergence of the continuous time plant is provided without making any assumption either the richness of the reference signals or on the existence of specific convex sets in which the estimated parameters belong or finally on the coprimeness of the polynomials describing the arma model as in known adaptive pole placement schemes

brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

reachability indices of periodic positive systems via positive shift similarity the problem of the paper is the formulation of the concept of reachability indices of periodic linear positive systems a positive system is one in which the positive orthant is an invariant subset with respect to positive input signals the concept of shift similarity for periodic positive systems is defined and the associated cyclically augmented system is considered the results are the relation of the positive similarity of both representations the formulation of the reachability indices and a detailed example

concolor constrained non convex low rank model for image deblocking due to independent and coarse quantization of transform coefficients in each block block based transform coding usually introduces visually annoying blocking artifacts at low bitrates which greatly prevents further bit reduction to alleviate the conflict between bit reduction and quality preservation deblocking as a post processing strategy is an attractive and promising solution without changing existing codec in this paper in order to reduce blocking artifacts and obtain high quality image image deblocking is formulated as an optimization problem within maximum a posteriori framework and a novel algorithm for image deblocking using constrained non convex low rank model is proposed the l p 0 penalty function is extended on singular values of a matrix to characterize low rank prior model rather than the nuclear norm while the quantization constraint is explicitly transformed into the feasible solution space to constrain the non convex low rank optimization moreover a new quantization noise model is developed and an alternatively minimizing strategy with adaptive parameter adjustment is developed to solve the proposed optimization problem this parameter free advantage enables the whole algorithm more attractive and practical experiments demonstrate that the proposed image deblocking algorithm outperforms the current state of the art methods in both the objective quality and the perceptual quality

a multirate digital controller for model matching abstract this paper presents a multirate digital controller which comprises a stable linear time invariant system with a multirate sampling scheme this controller is capable of arbitrary zero assignment pole assignment and model matching and it is applicable to plants with unstable zeros the stable controller also provides improved system intersample performance a controller design procedure is derived an example is given to illustrate the design and the system performance

optimal disturbance rejection control for nonlinear impulsive dynamical systems in this paper we develop an optimality based framework for addressing the problem of nonlinear nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances specifically we transform a given nonlinear nonquadratic hybrid performance criterion to account for system disturbances as a consequence the disturbance rejection problem is translatedinto an optimal hybridcontrol problem furthermore the resulting optimal hybrid control law is shown to render the closed loop nonlinear input output map dissipative with respect to general supply rates in addition the lyapunov function guaranteeing closed loop stability is shown to be a solution to a stead y state hybridhamilton jacobi isaacs equation andthus guaranteeing optimality 2005 elsevier ltd all rights reserved

stochastic stability and robust control for sampled data systems with markovian jump parameters in this paper the problems of stochastic stability and robust control for a class of uncertain sampled data systems are studied the systems consist of random jumping parameters described by finite state semi markov process sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented the conditions for the existence of a sampled data feedback control and a multirate sampled data optimal control for the continuous time uncertain markovian jump systems are also obtained the design procedure for robust multirate sampled data control is formulated as linear matrix inequalities lmis which can be solved efficiently by available software toolboxes finally a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques

lqg optimal control of multirate sampled data systems an lqg control synthesis technique for multirate sampled data systems where each input has its own frequency of updating and each output has its own frequency of measurement is presented the skew of the output sampling mechanism renders the prediction problem singular for the lack of measures at some time instants an ad hoc prediction algorithm is derived by enlarging the dimension of the state vector to be estimated and feeding the state filter with a combination of measured outputs over a past and finite interval of time the constraints on the input updating mechanism are dealt with by inserting a dynamical system corresponding to a zero order hold into the loop

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

gain margin improvement using generalized sampled data hold function based multirate output compensator abstract for a siso strictly proper nonminimum phase continuous time linear time invariant lti plant it was shown in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr that the closed loop gain margin obtained via a generalized sampled data hold function gshf based dynamic compensator is significantly improved over that achieved via a conventional periodic controller used in francis b a and t t georgiou 1988 ieee trans automat contr ac 33 820 832 nevertheless the compensator so designed is not necessarily strictly proper it is well known that it is practically difficult and sometimes impossible to implement a nonstrictly proper compensator due to the requirement of zero computation time further as has been shown in vidyasagar m 1985 systems and control letters 5 413 418 stabilization by a nonstrictly proper controller is never robust against singular perturbations in this paper we propose a new type of gshf based compensator which employs multirate sampling of the plant output using the proposed compensator not only the same level of gain margin as in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr can be achieved but also more importantly the compensator is strictly proper

some qualitative properties of sampled data control systems the authors consider sampled data control systems which consist of an interconnection of a continuous time nonlinear plant and a digital controller which has quantizers but is otherwise linear along with the required interface elements a d and d a converters in the present paper the authors study the qualitative effects of the quantizers and the plant nonlinearities of these systems

some qualitative properties of multirate digital control systems the authors consider multirate digital control systems which consist of an interconnection of a continuous time nonlinear plant described by ordinary differential equations a digital controller described by ordinary difference equations which has quantizers but is otherwise linear along with the required interface elements a d and d a converters the input to the digital controller consists of the multirate sampled output of the plant in the present paper the authors show that when quantizer nonlinearities are neglected then under reasonable conditions which exclude the critical cases the stability properties in the lyapunov sense of the trivial solution of a nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization for such systems we also present a result concerning the existence and construction of stabilizing multirate output digital controllers in the present paper the authors also show that the solutions of a multirate digital feedback control system with nonlinear plant and quantizers are uniformly ultimately bounded if the trivial solution of the corresponding linear system consisting of the linearization of the plant and with the quantization removed from the digital controller is asymptotically stable we also provide a result which compares the response of multirate digital control systems with nonlinear plant and quantizers in the controller with the response of the corresponding nonlinear multirate digital control systems without quantizers in the digital controller

an estimation algorithm for multirate sampled digital control systems abstract this paper presents an optimization based algorithm for state estimation of multirate digital control systems the algorithm features a predictor estimator structure and it is derived by employing a time invariant modelling approach to multirate systems special care is taken to ensure the causality of the derived estimation algorithm and to reduce the dimensionality inherent in multirate system modelling while maintaining a reasonably simple implementation the proposed algorithm is developed to ensure convergence in state estimation between base sampling instants as well as between model rate sampling instants

pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images the shape adaptive discrete cosine transform sa dct transform can be computed on a support of arbitrary shape but retains a computational complexity comparable to that of the usual separable block dct b dct despite the near optimal decorrelation and energy compaction properties application of the sa dct has been rather limited targeted nearly exclusively to video compression in this paper we present a novel approach to image filtering based on the sa dct we use the sa dct in conjunction with the anisotropic local polynomial approximation intersection of confidence intervals technique which defines the shape of the transform s support in a pointwise adaptive manner the thresholded or attenuated sa dct coefficients are used to reconstruct a local estimate of the signal within the adaptive shape support since supports corresponding to different points are in general overlapping the local estimates are averaged together using adaptive weights that depend on the region s statistics this approach can be used for various image processing tasks in this paper we consider in particular image denoising and image deblocking and deringing from block dct compression a special structural constraint in luminance chrominance space is also proposed to enable an accurate filtering of color images simulation experiments show a state of the art quality of the final estimate both in terms of objective criteria and visual appearance thanks to the adaptive support reconstructed edges are clean and no unpleasant ringing artifacts are introduced by the fitted transform

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

postprocessing of low bit rate block dct coded images based on a fields of experts prior transform coding using the discrete cosine transform dct has been widely used in image and video coding standards but at low bit rates the coded images suffer from severe visual distortions which prevent further bit reduction postprocessing can reduce these distortions and alleviate the conflict between bit rate reduction and quality preservation viewing postprocessing as an inverse problem we propose to solve it by the maximum a posteriori criterion the distortion caused by coding is modeled as additive spatially correlated gaussian noise while the original image is modeled as a high order markov random field based on the fields of experts framework experimental results show that the proposed method in most cases achieves higher psnr gain than other methods and the processed images possess good visual quality in addition we examine the noise model used and its parameter setting the noise model assumes that the dct coefficients and their quantization errors are independent this assumption is no longer valid when the coefficients are truncated we explain how this problem can be rectified using the current parameter setting

estimation using a multirate filter this note presents both optimal and suboptimal filtering algorithms for estimating state variables based on measurements sampled at two different data rates the optimal algorithm consists of two parallel kalman filters one processes the fast rate measurement and is of reduced order and the other processes the residuals from the first filter along with the slow rate measurement this algorithm is used to design a suboptimal algorithm that has decreased computational requirements with only a small performance penalty

two delay robust digital control and its applications avoiding the problem on unstable limiting zeros in the design of linear control systems the existence of unstable zeros makes it difficult to construct many control systems when the usual digital control scheme is used unstable zeros appear in the discrete time model due to the existence of limiting zeros even though the continuous time plant is minimal phase to avoid this unstable zero problem two new digital control schemes called two delay output control and two delay input control are proposed these control systems are proved to have no finite zeros asymptotic inverse systems pole assignable unknown input observers and output feedback controllers having the ltr loop transfer recovery property are developed using the two delay output control zero assignable control systems and model matching control systems are developed using the two delay input control

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

compression artifact reduction by overlapped block transform coefficient estimation with block similarity block transform coded images usually suffer from annoying artifacts at low bit rates caused by the coarse quantization of transform coefficients in this paper we propose a new method to reduce compression artifacts by the overlapped block transform coefficient estimation from non local blocks in the proposed method the discrete cosine transform coefficients of each block are estimated by adaptively fusing two prediction values based on their reliabilities one prediction is the quantized values of coefficients decoded from the compressed bitstream whose reliability is determined by quantization steps the other prediction is the weighted average of the coefficients in nonlocal blocks whose reliability depends on the variance of the coefficients in these blocks the weights are used to distinguish the effectiveness of the coefficients in nonlocal blocks to predict original coefficients and are determined by block similarity in transform domain to solve the optimization problem the overlapped blocks are divided into several subsets each subset contains nonoverlapped blocks covering the whole image and is optimized independently therefore the overall optimization is reduced to a set of sub optimization problems which can be easily solved finally we provide a strategy for parameter selection based on the compression levels experimental results show that the proposed method can remarkably reduce compression artifacts and significantly improve both the subjective and objective qualities of block transform coded images

almost sure exponential stabilization by discrete time stochastic feedback control given an unstable linear scalar differential equation dot x t alpha x t alpha 0 we will show that the discrete time stochastic feedback control sigma x t tau tau db t can stabilize it that is we will show that the stochastically controlled system dx t alpha x t dt sigma x t tau tau db t is almost surely exponentially stable when sigma 2 2 alpha and tau 0 is sufficiently small where b t is a brownian motion and t tau is the integer part of t tau we will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control the reason why we consider the discrete time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times say 0 tau 2 tau ldots for example where tau 0 is the duration between two consecutive observations accordingly the stochastic feedback control should be designed based on these discrete time observations namely the stochastic feedback control should be of the form sigma x t tau tau db t from the point of control cost it is cheaper if one only needs to observe the state less frequently it is therefore useful to give a bound on tau from below as larger as better

reduced rank regression via adaptive nuclear norm penalization we propose an adaptive nuclear norm penalization approach for low rank matrix approximation and use it to develop a new reduced rank estimation method for high dimensional multivariate regression the adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix and it is generally non convex under the natural restriction that the weight decreases with the singular value however we show that the proposed non convex penalized regression method has a global optimal solution obtained from an adaptively soft thresholded singular value decomposition the method is computationally efficient and the resulting solution path is continuous the rank consistency of and prediction estimation performance bounds for the estimator are established for a high dimensional asymptotic regime simulation studies and an application in genetics demonstrate its efficacy

a function space approach to sampled data control systems and tracking problems this paper presents a new framework for hybrid sampled data control systems instead of considering the state only at sampling instants this paper introduces a function piece during the sampling period as the state and gives an infinite dimensional model with such a state space this gives the advantage that sampled data systems with built in intersample behavior can be regarded as linear time invariant discrete time systems as a result the approach makes it possible to introduce such time invariant concepts as transfer functions poles and zeros to the sampled data systems even with the presence of the intersample behavior in particular tracking problems can be studied in this setting in a simple and unified way and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions this leads to the internal model principle for sampled data systems

low rank approximation via generalized reweighted iterative nuclear and frobenius norms the low rank approximation problem has recently attracted wide concern due to its excellent performance in real world applications such as image restoration traffic monitoring and face recognition compared with the classic nuclear norm the schatten p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world however schatten p norm minimization is a challenging non convex non smooth and non lipschitz problem in this paper inspired by the reweighted ell 1 and ell 2 norm for compressive sensing the generalized iterative reweighted nuclear norm girnn and the generalized iterative reweighted frobenius norm girfn algorithms are proposed to approximate schatten p norm minimization by involving the proposed algorithms the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems in addition we prove that both proposed algorithms converge at a linear rate to a bounded optimum numerical experiments for the practical matrix completion mc robust principal component analysis rpca and image decomposition problems are illustrated to validate the superior performance of both algorithms over some common state of the art methods

a note on generalized hold functions abstract in this note we study the generalized hold functions for use of digital control of continuous time systems first we define and solve the problem of simultaneous stabilization and minimization it is shown that every plant with a strictly proper transfer function is simultaneously stabilizable and minimizable provided that the sampling interval is small enough we also consider robust designs of generalized hold functions a condition is given for the stability of a system using generalized hold functions in the presence of uncertainty

technical communique stabilization of continuous time hybrid stochastic differential equations by discrete time feedback control in this paper we are concerned with the mean square exponential stabilization of continuous time hybrid stochastic differential equations also known as stochastic differential equations with the markovian switching by discrete time feedback controls although the stabilization by continuous time feedback controls for such equations has been discussed by several authors see e g ji and chizeck 1990 mao lam and huang 2008 mao yin and yuan 2007 wu shi and gao 2010 wu su and shi 2012 there is so far no result on the stabilization by discrete time feedback controls our aim here is to initiate the study in this area by establishing some new results

projection based spatially adaptive reconstruction of block transform compressed images at the present time block transform coding is probably the most popular approach for image compression for this approach the compressed images are decoded using only the transmitted transform data we formulate image decoding as an image recovery problem according to this approach the decoded image is reconstructed using not only the transmitted data but in addition the prior knowledge that images before compression do not display between block discontinuities a spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets apart from the data constraint set this algorithm uses another new constraint set that enforces between block smoothness the novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics a simplified spatially adaptive recovery algorithm is also proposed and the analysis of its computational complexity is presented numerical experiments are shown that demonstrate that the proposed algorithms work better than both the jpeg deblocking recommendation and our previous projection based image decoding approach

on improving density estimators which are not bona fide functions in order to improve the rate of decrease of the imse for nonparametric kernel density estimators with nonrandom bandwidth beyond o n 4 5 all current methods must relax the constraint that the density estimate be a bona fide function that is be nonnegative and integrate to one in this paper we show how to achieve similar improvement without relaxing any of these constraints the method can also be applied for orthogonal series adaptive orthogonal series spline jackknife and other density estimators and assures an improvement of the imse for each sample size

periodically varying compensation of time invariant systems linear time invariant discrete time scalar systems under periodically varying output feedback and the associated problems of stabilization and arbitrary eigenvalue assignment are investigated the general form of the characteristic polynomial of the closed loop periodically varying system is obtained and some detailed results are provided for the second order case interesting research questions are pointed out

removal of compression artifacts using projections onto convex sets and line process modeling we present a new image recovery algorithm to remove in addition to blocking ringing artifacts from compressed images and video this new algorithm is based on the theory of projections onto convex sets pocs a new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure the definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying to overcome the numerical difficulty in computing the projections onto these sets a divide and conquer dac strategy is introduced according to this strategy new smoothness sets are derived such that their projections are easier to compute the effectiveness of the proposed algorithm is demonstrated through numerical experiments using motion picture expert group based mpeg based coders decoders codecs

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

fixed order sampled data estimation for the kalman filter type sampled data estimation problem utilizing an averaging a d device the equivalent discrete time problem is shown to be of increased order the fixed structure optimal projection approach for reduced order discrete time estimation is applied to the equivalent discrete time problem in order to characterize reduced order estimators

analysis of decorrelation transform gain for uncoded wireless image and video communication an uncoded transmission scheme called softcast has recently shown great potential for wireless video transmission unlike conventional approaches softcast processes input images only by a series of transformations and modulates the coefficients directly to a dense constellation for transmission the transmission is uncoded and lossy in nature with its noise level commensurate with the channel condition this paper presents a theoretical analysis for an uncoded visual communication focusing on developing a quantitative measurements for the efficiency of decorrelation transform in a generalized uncoded transmission framework our analysis reveals that the energy distribution among signal elements is critical for the efficiency of uncoded transmission a decorrelation transform can potentially bring a significant performance gain by boosting the energy diversity in signal representation numerical results on markov random process and real image and video signals are reported to evaluate the performance gain of using different transforms in uncoded transmission the analysis presented in this paper is verified by simulated softcast transmissions this provide guidelines for designing efficient uncoded video transmission schemes

multi 2 rate control from a 2 periodic perspective generalized 2 rate control this technical note finds that a conventional 2 rate controller which receives feedback at t but provides control at 2t intervals has a 2 periodic core and augments this core to have a generalized 2 rate control that has complete loop zero and pole placement capability an algorithm for controller parameter evaluation for pole zero placement using only linear algebraic steps has been developed the controller also ensures zero steady state and improved transient ripples its superiority in respect of gain margin compensation is illustrated for a third order plant with an unstable pole and a non minimum phase zero

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

a new optimal multirate control of linear periodic and time invariant systems the optimal multirate design of linear continuous time periodic and time invariant systems is considered it is based on solving the continuous linear quadratic regulation lqr problem with the control being constrained to a certain piecewise constant feedback necessary and sufficient conditions for the asymptotic stability of the resulting closed loop system are given an explicit multirate feedback law that requires the solution of an algebraic discrete riccati equation is presented such control is simple and can be easily implemented by digital computers when applied to linear time invariant systems multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly compared to the classical single rate sampled data feedback in which the state is always sampled at the same rate the multirate system can provide a better response with a considerable reduction in the optimal cost in general the multirate scheme offers more flexibility in choosing the sampling rates

orthogonal polynomials random matrices and the numerical inversion of the laplace transform of positive functions a method for the numerical inversion of the laplace transform of a continuous positive function f t is proposed random matrices distributed according to a gibbs law whose energy v x is a function of f t are considered as well as random polynomials orthogonal with respect to w x e v x the equation relating w x to the reproducing kernel and to the condensed density of the roots of the random orthogonal polynomials is exploited basic results from the theories of orthogonal polynomials random matrices and random polynomials are revisited in order to provide a unified and almost self contained context the qualitative behavior of the solutions provided by the proposed method is illustrated by numerical examples and discussed by using logarithmic potentials with external fields that give insight into the asymptotic behavior of the condensed density when the number of data points goes to infinity

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

combined parameter and output estimation of dual rate systems using an auxiliary model for a dual rate sampled data system an auxiliary model based identification algorithm for combined parameter and output estimation is proposed the basic idea is to use an auxiliary model to estimate the unknown noise free output true output of the system and directly to identify the parameters of the underlying fast single rate model from the dual rate input output data it is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance and that the output estimates uniformly converge to the true outputs an example is included

image denoising via bandwise adaptive modeling and regularization exploiting nonlocal similarity this paper proposes a new image denoising algorithm based on adaptive signal modeling and regularization it improves the quality of images by regularizing each image patch using bandwise distribution modeling in transform domain instead of using a global model for all the patches in an image it employs content dependent adaptive models to address the non stationarity of image signals and also the diversity among different transform bands the distribution model is adaptively estimated for each patch individually it varies from one patch location to another and also varies for different bands in particular we consider the estimated distribution to have non zero expectation to estimate the expectation and variance parameters for every band of a particular patch we exploit the nonlocal correlation in image to collect a set of highly similar patches as the data samples to form the distribution irrelevant patches are excluded so that such adaptively learned model is more accurate than a global one the image is ultimately restored via bandwise adaptive soft thresholding based on a laplacian approximation of the distribution of similar patch group transform coefficients experimental results demonstrate that the proposed scheme outperforms several state of the art denoising methods in both the objective and the perceptual qualities

multistage linear estimation using partitioning the estimation algorithm described in this note solves the linear estimation problem as a two stage estimator consisting of two consecutive kalman filters the interconnections between this estimator structure and the more familiar one stage optimal kalman filter are discussed applications to decentralized estimation bias estimation and parameter identification are described

receding horizon recursive state estimation describes a receding horizon discrete time state observer using the deterministic least squares framework the state estimation horizon which determines the number of past measurement samples used to reconstruct the state vector is introduced as a tuning parameter for the proposed state observer a stability result concerning the choice of the state estimation horizon is established it is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

inherent design limitations for linear sampled data feedback systems there is a well developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller this theory describes limitations on achievable performance present when the plant has non minimum phase zeros unstable poles and or time delays the parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants this paper develops a theory of design limitations for sampled data feedback systems wherein the response of the analogue system output is considered this is done using the fact that the steady state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental this fact allows fundamental sensitivity and complementary sensitivity functions that re

multi rate optimal state estimation this article formulates a multi rate linear minimum mean squared error lmmse state estimation problem which includes four rates as follows the state updating rate in the model the measurement sampling rate the estimate updating rate and the estimate output rate this formulation is unique in two ways first the rate ratio between state measurement and state estimate is more general a rational number instead of just an integer or its reciprocal as considered in the existing literature second state estimates are produced in blocks which have never been considered before in the multi rate estimator design the multi rate lmmse estimation problem is solved by examining several distinctive cases for single rate state estimation obtained through the lifting technique also sufficient conditions are given for asymptotic stability of the proposed multi rate lmmse estimators an example in tracking a manoeuvering target is given to illustrate the proposed multi rate state estimators

block form control of linear time invariant discrete time systems defined over commutative rings abstract a new approach based on a block input block output state model is developed for the study of linear time invariant discrete time systems whose coefficients belong to a commutative ring with 1 it is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems by time compressing the block input state representation new results are obtained on the construction of a memoryless block form state feedback control law that yields a type of assignability and or deadbeat control these results are then dualized to yield results on a new type of state observer based on a block of output measurements the observer and state feedback controller are then combined to yield new results on input output regulation and set point tracking for systems defined over an arbitrary commutative ring in the last part of the paper the block input form is utilized to study the stabilization of systems defined over a normed algebra

discretized and interpolated kernel density estimates abstract the kernel estimate of a probability density function inherits its smoothness properties from the kernel density chosen by the investigator nevertheless for computational and especially graphical reasons exact kernel density estimates are often presented in piecewise constant discretized or piecewise linear interpolated form using the exact estimate only at some grid of points the asymptotic integrated mean squared error properties of these modifications are studied it is seen that discretization may adversely affect the order of magnitude of this risk criterion so care needs to be taken in practice to limit the degree of discretization employed this roughness effect essentially disappears when interpolation is used instead then it takes a remarkably coarse grid to result in more than a negligible deterioration in the estimate s performance data discretization prior to applying the kernel density estimation prescription is also addressed such prebinning does not affect the smoot

model predictive control of multi rate sampled data systems a state space approach a model predictive control mpc technique is developed for systems with measurements available at different sampling rates the method uses general state space system representations that incorporate secondary measurements as well as primary measurements the optimal multi rate mr filtering method is used to develop prediction equations for mpc a simple suboptimal cascade filter is also proposed for dual rate dr systems where the primary measurements are available at a slow rate and the secondary measurements are available at a fast rate in addition to significant reduction in filter gain computation requirements the suboptimal filtering strategy offers superior primary measurement failure tolerance the applicability of the proposed methods to realistic systems is demonstrated through an example application to a high purity distillation column

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

generalized lyapunov and invariant set theorems for nonlinear dynamical systems in this paper we develop generalized lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the lyapunov function and the system dynamics are removed in particular local and global stability theorems are given using lower semicontinuous lyapunov functions furthermore generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized lyapunov level surfaces the proposed results provide transparent generalizations to standard lyapunov and invariant set theorems

structural properties of a class of linear hybrid systems and output feedback stabilization in this paper we deal with the problem of output feedback stabilization for a class of linear hybrid systems this problem is addressed by characterizing the structural properties of such a class of systems namely reachability controllability stabilizability observability constructibility and detectability are framed in terms of algebraic and geometric conditions on the data of the system two canonical forms recalling the classical kalman decompositions with respect to reachability and observability are given by taking advantage of this characterization duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time invariant output feedback compensator are stated compared with previous results no assumption is needed on the plant about minimum phaseness relative degree or squareness

the influence of rounding errors on some nonparametric estimators of a density and its derivatives all continuous data is rounded to some extent and this rounding introduces errors into the estimation of the parent density and its derivatives in this paper we examine the influence of rounding errors on the two most popular types of nonparametric density estimator those based on kernels and those based on generalized fourier series our results lead directly to several important conclusions which are very relevant to the practical problems of density estimation

improving computational efficiency of model predictive control algorithm using wavelet transformation we propose an mpc algorithm with desirable stability and constraint handling properties yet which retains computational simplicity the closed loop stability and constraint handling are achieved b

frequency polygons theory and application abstract in this article i investigate the theoretical properties and applications of the frequency polygon which is constructed by connecting with straight lines the mid bin values of a histogram for estimating an unknown probability density function using a random sample the frequency polygon is shown to dominate the histogram with respect to the criterion of integrated mean squared error achieving the same rate of convergence to zero of the integrated mean squared error as non negative kernel estimators data based algorithms for constructing frequency polygons are discussed and illustrated one is based on a histogram with bin width equal to 2 15sn 1 5 where s is an estimate of the standard deviation from a sample of size n another approach is based on the method of generalized crossvalidation the bivariate frequency polygon is also investigated comparisons are made between the frequency polygon and other density estimators examples with data in one and two dimensions are presented

a dual rate digital compensator for zero assignment abstract this paper considers design of a simple dual rate digital compensator drdc for assignment of system zeros the drdc comprises a linear time invariant system with a dual rate sampling scheme it is shown that zeros of a discrete system can be arbitrarilassigned by drdc corresponding to the block sampling period and that drdc is applicable to non minimum phase plants a design procedure and an example are given

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

optimal hold functions for sampled data regulation abstract this paper investigates the use of generalized sampled data hold function control gshf to optimize quadratic measures of performance in sampled data control loops the idea of gshf control is to use sampled data feedback but consider the hold function as a design parameter explicit solutions are given for the gshf versions of the optimal lq and lqg regulators the questions of existence uniqueness and computation of optimal hold functions are treated an example is presented

multirate robust digital control for fuzzy systems with periodic lyapunov function sampled data control which is capable of stabilizing general nonlinear systems is of great current interest in this paper the takagi sugeno ts fuzzy model is used to represent the nonlinear plant the paper is primarily concerned with designing digital controllers for the ts fuzzy continuous time model to stabilize the closed loop system in the problem formulation we only assume that the sampled values at a sampling rate of 1 t sub s are available for control within the sampling intervals the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series this digital control action is then fed into the nonlinear system through a zero order holder in this paper two kinds of digital controllers are designed multirate and single rate digital controllers within a sampling interval the single rate controller is static while the multirate controller is periodically time varying i e the control action is switched at a small switching period t clearly for the single rate case this switching period t is equal to the sampling period t sub s this paper presents a design procedure for the multirate fuzzy controller with the single rate control as a special case the results are formulated as linear matrix inequalities numerical example shows the effectiveness of the proposed design procedures

hybrid output feedback stabilization for lti systems with single output this note presents a hybrid control scheme for a class of continuous time lti systems that cannot be stabilized by a single static output feedback sof controller the main idea here is to design multiple sof gains and proper logic rules that orchestrate switching among these gains so as to achieve the global stability one challenge however is that the switching logic should be in the output feedback form as well this may seriously restrict the possible choices of switching surfaces especially when the output is just a scalar to overcome this difficulty a multirate sampling control scheme is proposed under this framework a hybrid output feedback stabilizing controller is designed and sufficient controller synthesis conditions are proposed as linear matrix inequalities based on multiple lyapunov function theorems the note concludes with a discussion on possible extensions and future research topics

achieving higher order convergence rates for density estimation with binned data abstract a method is proposed for achieving fast o n 8 9 and faster asymptotic mean integrated squared error amise convergence rates in density estimation using data condensed to standard histogram bin counts and edges the method involves the two elements of b splines and the correct mass proportions property in which the probability mass for the histogram bins equals exactly the fraction of the data found in those bins it is shown that the asymptotic bias of such an estimate using a spline of order p and bin width h will be o hp resulting in optimal amise of o n 2p 2p 1 form theoretical and numeric comparisons to kernel based and other estimators show that the histospline estimator is usually comparable and often superior an extension to the multivariate density estimation setting is described

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

brief paper a state space gpc with extensions to multirate control a state space formulation for generalized predictive control gpc is presented unlike other state space formulations we derive both the state feedback controller and state estimator gains using a least squares framework the present formulation provides a set of consistent design choices for both the controller and the state estimator design it also encapsulates both single rate and multirate controllers in the same algorithm it is argued that such a design approach can be advantageous especially when the control algorithm is required to tolerate sensor failure the generality of the design method is illustrated by synthesizing two well known multirate control algorithms a link with the generalized sampled data hold function is also established

performance study of multi rate output controllers under noise disturbances this paper presents a comparative study of the performance of a multi rate output controller mroc with a linear quadratic gaussian lqg controller in the presence of noise disturbances and anti aliasing filters the basis of comparison is to apply an lqg law with a one step ahead prediction type kalman filter hereafter called lqg law i and an lqg law with a current estimation type kalman filter hereafter called lqg law ii to a linear time invariant continuous time plant model with a white gaussian process and measurement noise and compute a linear quadratic performance index for the discretized plant equivalent noise matrices for using the mroc law are derived and the same quadratic performance index computed in order to have a fair comparison the cut off frequency of the anti aliasing filter used to remove high frequency noise components prior to sampling is also kept the same when applying both laws application of both laws in typical situations shows that the performance of the mroc law is w

strong stabilization with infinite multivariable gain margin through linear periodic control the problem of the strong stabilization with infinite gain margin with the additional requirement of a prescribed rate of convergence of the free responses is addressed for linear time invariant discrete time multivariable plants in the case when unknown different scalar gains act either on the inputs or on the outputs necessary and sufficient conditions for the solvability of the problem by means of a stable linear periodic discrete time output feedback dynamic controller are derived algorithmic procedures are given for designing the proposed periodic controllers

theory of projection onto the narrow quantization constraint set and its application since the postprocessing of coded images using a priori information depends on the constraints imposed on the coded images it is important to utilize constraints that are best suited to postprocessing techniques among the constraint sets the quantization constraint set qcs is commonly used in the iterative algorithms that are especially based on the theory of projections onto convex sets pocs the converged image in the iteration is usually a boundary point of the qcs but we can easily conjecture that the possible location of the original image is inside the qcs in order to obtain an image inside the qcs we proposed a new convex constraint set a subset of the qcs called narrow qcs nqcs as a substitute for the qcs in order to demonstrate that the nqcs works better than the qcs on natural images we present mathematical analysis with examples and simulations by reformulating the iterative algorithm of the constrained minimization problem or of the pocs using the probability theory since the initial image of the iteration is the centroid of the qcs we reach a conclusion that the first iteration is enough to recover the coded image which implies no need of any theories that guarantee the convergences